International arbitrage and the extensive margin of tradebetween rich and poor countries∗

Reto Foellmi†, Christian Hepenstrick‡, Josef Zweimüller§

February 9, 2017

forthcoming in: Review of Economic Studies

Abstract

We incorporate consumption indivisibilities into the Krugman (1980) model and showthat an importer’s per capita income becomes a primary determinant of “export zeros”.Households in the rich North (poor South) are willing to pay high (low) prices for con-sumer goods; hence unconstrained monopoly pricing generates arbitrage opportunities forinternationally traded products. Export zeros arise because some northern firms abstainfrom exporting to the South, to avoid international arbitrage. Rich countries benefit froma trade liberalization, while poor countries lose. These results hold also under more generalpreferences with both extensive and intensive consumption margins. We show that a stan-dard calibrated trade model (that ignores arbitrage) generates predictions on relative pricesthat violate no-arbitrage constraints in many bilateral trade relations. This suggests thatinternational arbitrage is potentially important.

JEL classification: F10, F12, F19Keywords: Non-homothetic preferences, parallel imports, arbitrage, extensive margin, ex-

port zeros

∗We thank Sandro Favre, Patrick DeCaes, Stefan Legge, Damian Osterwalder and Marco Schmid for excel-lent research assistance. We are grateful to Claudia Bernasconi for generous help in preparing and checking theComtrade data and Michael Waugh for access to the data used in section 7 of the paper. We are particularlygrateful to two anonymous referees, Olivier Blanchard, Josef Falkinger, Gene Grossman, Wilhelm Kohler andMarc Melitz for encouraging and very helpful comments. Financial support by the Swiss National Science Foun-dation (SNF) through the Sinergia-projects CRSI11_132272 “Economic Inequality and International Trade“ andCRSII1_154446 “Inequality and Globalization: Demand versus Supply Forces and Local Outcomes” is gratefullyacknowledged. The views, opinions, findings, and conclusions or recommendations expressed in this paper arestrictly those of the authors. They do not necessarily reflect the views of the Swiss National Bank.

†University of St. Gallen and CEPR, SIAW-HSG, Bodanstrasse 8, CH-9000 St.Gallen, Tel: +41 71 224 22 69,Fax: +41 71 224 22 98, email: reto.foellmi@unisg.ch.

‡Swiss National Bank and University of Zurich, Boersenstrasse 15 Postfach, CH-8022 Zuerich, e-mail: Chris-tian.Hepenstrick@snb.ch§University of Zurich and CEPR, Department of Economics, Schoenberggasse 1, CH - 8001 Zuerich, Tel: +41

44 634 37 24, Fax: +41 44 634 49 07, e-mail: josef.zweimueller@econ.uzh.ch. Josef Zweimüller is also associatedwith CESifo and IZA.

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1 Introduction

We study a model of international trade in which an importer’s per capita income is a primarydeterminant of the extensive margin of international trade. Two facts motivate our analysis.First, there are huge differences in per capita incomes across the globe and these differences mayhave important consequences for patterns of international trade via the demand side. Second,per capita incomes of destination countries correlate strongly with the extensive margin of trade.In 2007, for example, the probability that the US exports a given HS 6-digit product to a high-income country was 63.4 percent, while the export probabilities to upper-middle, lower-middle,and low-income destinations were only 48.8 percent, 36.6 percent, and 13.6 percent, respectively.Furthermore, also US firm-level data show a positive correlation between export probabilitiesand destinations’ per capita incomes (Bernard, Jensen, and Schott 2009).

Recent research has emphasized the presence of “zeros” in bilateral trade data, see e.g. Help-man, Melitz, and Rubinstein (2007) at the country pair level; Hummels and Klenow (2005) atthe product level; and Bernard, Jensen, Redding, and Schott (2007) at the firm level. However,the literature did not systematically explore the role of per capita incomes. The standard expla-nation for export zeros relies on heterogeneous firms and fixed export-market entry costs (Melitz2003, Chaney 2008, Arkolakis, Costinot and Rodriguez-Clare 2012). Export zeros arise if a firm’smarginal costs are too high and/or export market size (in terms of aggregate GDP) is too lowto cover the fixed export costs.1 Importantly, there is no separate role for per capita incomes.Because of homothetic preferences it is irrelevant whether a given aggregate GDP arises from alarge population and a low per capita income, or vice versa.2

Our paper provides an alternative approach to explain export zeros in which the demandside plays the crucial role. In particular, we elaborate the idea that low per capita incomesare associated with low willingnesses to pay for differentiated products, so that firms abstainfrom exporting to poor destinations. Our emphasis on the demand channel does not only leadto new predictions on trade patterns. It has also important implications for consumer welfare.Our model predicts that poor countries may lose from a trade liberalization, while rich countriesalways gain. This is different from standard models where gains from trade are more evenlydistributed and all trading partners typically benefit from a trade liberalization.

We start out with a simple model that is identical to the basic Krugman (1980) framework,except that consumer goods are indivisible and households purchase either one unit of a particularproduct or do not purchase it at all. Such “0-1” preferences generate, in a straightforward way, asituation where a household’s willingness to pay for differentiated products depends on householdincome. However, 0-1 preferences are very stylized, as households can adjust their consumptionin response to price and income changes only through the extensive margin.3 We then show that

1This heterogeneous-firm framework has proven to be useful in explaining firm-level evidence on export be-havior. For a recent survey, see Bernard, Jensen, Redding, and Schott (2012).

2Baldwin and Harrigan (2011) find that real GDP per worker in the destination country is a significantdeterminant of zeros in US export data. While they consider real GDP per worker as a demand-related control,they do not systematically explore this result in the context of their theoretical model (which sticks to theassumption of homothetic preferences).

3Notice that “0-1” preferences and CES preferences can be considered as two polar cases. With 0-1 preferences,optimal consumption responds only along the extensive margin; with CES-preferences consumption responds only

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the qualitative results of the 0-1 model carry over to more general settings where consumptionis allowed to respond both along the extensive and the intensive margin.

Our paper makes two key contributions. The first is the recognition that firms from richcountries might not export to a poor country due to a threat of international arbitrage. Considera US firm that sells its product both in the US and in China. Suppose this firm charges a pricein China equal to the Chinese households’ (low) willingness to pay and a price in the US equalto the US households’ (high) willingness to pay. When price differences are large, arbitrageopportunities emerge: arbitrageurs can purchase the good cheaply on the Chinese market, shipit back to the US, and underbid local US producers. In equilibrium, US firms anticipate thethreat of arbitrage and will adjust accordingly. To avoid arbitrage, a US exporter has basicallytwo options: (i) charge a price in the US sufficiently low to eliminate arbitrage incentives; or (ii)abstain from selling the product in China (and other equally poor countries) thus eliminatingarbitrage opportunities. These two options involve a trade-off between market size and prices:firms that export globally have a large market but need to charge a low price; firms that sellexclusively on the US market (and in other equally rich countries) can charge a high price buthave a small market. In an equilibrium with ex-ante identical firms, the two options yield thesame profit.

The second key contribution of our paper relates to gains from trade and the welfare effectsof trade liberalizations. When per capita income gaps are small, firms are not constrained byarbitrage, and all goods are traded. In such a “full trade equilibrium”, lower trade costs increasewelfare in both countries. Lower losses during transport provide resources for production of morevarieties from which consumers in both countries benefit. In the more interesting case of largeper capita income gaps, firms are constrained by arbitrage, and not all goods are exported to thepoor country. In such an “arbitrage equilibrium” lower trade costs increase welfare in the richcountry but decrease welfare in the poor country. The reason is that lower trade costs tightenthe arbitrage constraint. With lower trade costs, globally active firms in the rich country needto reduce prices on their home market. This will induce more firms to abstain from exporting topoor countries, thus avoiding international arbitrage. As a result, fewer varieties are exportedto poor countries leading to lower consumption and welfare in these countries.

Our analysis highlights three further points. First, we make precise the differential conse-quences of an increase in aggregate GDP due to a higher per capita income and due to a largerpopulation. A higher per capita income in the South raises poor households’ willingness to pay,increasing northern firms’ incentive to sell their products internationally. In equilibrium, a largerfraction of northern firms export their product to the South. In contrast, a larger population inthe South leaves southern households’ demand for varieties unchanged but allows for the produc-tion of more varieties. This increases the world’s per capita consumption due to a scale effect;increases the volume of trade; and may or may not increase trade intensity. Moreover, a largerpopulation in the poor country may or may not increase the probability that a northern firmexports to the South. In sum, our model predicts that per capita income has a stronger effect

along the intensive margin (because Inada conditions induce households to consume all goods, irrespective of pricesand income). Clearly, the realistic scenario is in between these polar cases. We look at this case in Section 5.

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than population size on the probability that a northern firm exports to the South.A second point shows that the result of detrimental effects of trade liberalizations (on a

poor country’s welfare) needs to be qualified in a multi-country setting. When there are manyrich and many poor countries, a multilateral trade liberalization still reduces North-South tradedue to tighter arbitrage. However, it also stimulates South-South trade because the arbitrageconstraint is not binding among trading partners with similar per capita incomes. Hence amultilateral trade liberalization increases the welfare of poor households if the increase in South-South trade overcompensates the fall in North-South trade. The multi-country setting is alsouseful because it delivers empirical predictions. The main prediction (on which we shed lightempirically) is that a northern firm has a high probability to export to other northern countries,while the probability that it exports to a southern country is significantly lower and decreasesin the per capita income gap between the North and South.

A third point analyzes the conditions under which the basic logic of our 0-1 preferencescarries over to general (additive) preferences that allow for both an extensive and intensivemargin of consumption. We assume a general, additive subutility function v(c) and make precisethe conditions on v(c) under which international arbitrage can emerge. If these conditions aremet, there will be export zeros, provided that per capita income differences between the tradingpartners are sufficiently large. In this sense, the predictions of the simple 0-1 model hold alsounder more general preferences.

There is compelling evidence that threats of arbitrage affect the pricing decisions of firms inmany markets. Pharmaceutical industries are most prominent examples (WHO 2001, Ganslandtand Maskus 2004, Goldberg 2010). The WHO (2001) report argues that restraints on paralleltrade between poor and rich countries would allow companies to supply the former. Consequently,a key WHO recommendation is a more comprehensive implementation of differential pricingstrategies. Parallel trade is also relevant in other industries such as cars (Lutz 2004, Yeung andMok 2013), consumer electronics (Feng 2013), DVDs and cinemas (Burgess and Evans 2005),and other markets, like clothing and cosmetics (NERA 1999).

To shed light on the quantitative relevance of the arbitrage channel, we proceed in twosteps. We first provide reduced-form evidence from disaggregated trade data. We find thatthere is a strong and quantitatively large association between the export probability (of theUS and other large countries) and the per capita income of a given destination (conditional onthe destination’s aggregate GDP and other commonly used determinants of international tradeflows). This reduced-form evidence is consistent with binding arbitrage constraints, but couldalso be explained by a cost constraint: firms abstain from exporting because the marginal costof exporting are too high.4

In a second step, we pursue a model-based approach to learn more about the potentialrelevance of arbitrage constraints. We start out with the framework of Simonovska (2015) whocharacterizes the general equilibrium in a world economy with many countries and heterogenous

4In the absence of fixed export costs, this requires a specification of preferences featuring a finite reservationprice which increases in the destination’s per capita income. When the destination is very poor the reservationprice is very low, and export zeros arise because the price does not cover the marginal costs associated withexporting to that destination. The specification in Simonovska (2015) satisfies these features.

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firms. She uses Stone-Geary preferences, which belong to the class of preferences where arbitrageconstraints may, in principle, become binding. In this quite general environment, Simonovska(2015) is able to come up with predictions for the relative price of a given product betweenany two locations – under the assumption that firms do not have to take arbitrage constraintsinto account when setting their prices. This suggests a simple consistency check to assess thequantitative importance of arbitrage: With (i) predictions on relative (unconstrained) pricesand (ii) estimates of trade costs between any two locations, we can assess whether arbitrageconstraints are violated in an equilibrium that does not take into account arbitrage. In thisnumerical exercise, we find that arbitrage constraints are indeed violated in many trade relations.

Our analysis contributes to the literature on parallel trade (surveyed in Maskus, 2000 andGanslandt and Maskus, 2007). In partial equilibrium models, the welfare effects of parallelimports in a rich country are typically ambiguous because there is a tradeoff between reducedinnovation incentives on the one side and lower prices for consumers on the other side. To seethe contrast, consider for example the recent contribution by Roy and Saggi (2012). They showthat in an international duopoly, parallel trade induces the southern firm to charge an abovemonopoly price in the South in order to be able to charge a high price in the North. Softercompetition in the North then induces the northern firm to sell only in its home market at ahigh price, which harms northern consumers. We show that considering the general equilibriumuncovers an opposing force working through the economy wide resource constraint: It is stilltrue that a subset of northern firms will find it optimal to sell only in their home market ata high price. But this means that less northern resources are used to produce goods for theSouth, which increases the numbers of available varieties in the North and thus welfare. So thewelfare effects of parallel trade rules go in the opposite direction when considering the generalequilibrium.

Our paper is also related to the pricing-to-market literature, which focuses on the cross-country dispersion of prices of tradable goods. Atkeson and Burstein (2008) generate pricing-to-market in a model with Cournot competition and variable mark-ups. However, their focus ison the interaction of market structure and changes in marginal costs rather than on per capitaincome effects. Hsieh and Klenow (2007), Manova and Zhang (2012), and Alessandria andKaboski (2011), among others, document that prices of tradable consumer goods show a strongpositive correlation with per capita incomes in cross-country data. The papers by Markusen(2013), Sauré (2010), Behrens and Murata (2012a,b) and Bekkers, Francois, and Manchin (2012)provide frameworks in which richer consumers are less price-sensitive, so mark-ups and pricesare higher in richer countries. Mrazova and Neary (2013) explore in a comprehensive way howdeviations from CES preferences affect equilibrium outcomes in the Krugman model.5 Variable

5Other related papers allowing for non-homothetic (or quasi-homothetic) preferences include Fajgelbaum,Grossman, and Helpman (2011), Hummels and Lugovskyy (2009), Desdoigts and Jaramillo (2009), Neary (2009),Melitz and Ottaviano (2008), Falkinger (1990), and Auer, Chaney and Sauré (2014). Many papers found em-pirical support for non-homotheticities, e.g. Hunter and Markusen (1988), Hunter (1991), Francois and Kaplan(1996), Choi, Hummels, and Xiang (2006), Dalgin, Mitra, and Trindade (2008), Fieler (2011), Hepenstrick andTarasov (2015), Bernasconi (2013). Caron, Fally and Markusen (2014) show that non-homothetic preferences arequantitatively important for explaining the observed correlation between income elasticities and skill intensitiesat the sectoral level, resolving a substantial part of “missing trade puzzle” between rich and poor countries.

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mark-ups and pricing-to-market driven by per capita income are also a crucial feature in ourframework. Our paper extends this literature by showing that export zeros arise from the (threatof) international arbitrage, a feature not considered in previous papers.

The presence of a trade participation margin links the present paper to a recent literaturethat builds on Melitz (2003) and explores demand- and/or market-size effects in the context ofheterogeneous firm models. Arkolakis (2010) incorporates marketing costs into that framework,generating an effect of population size on export markets in addition to aggregate income. Eaton,Kortum, and Kramarz (2011) extend this framework, allowing for demand shocks (in additionto cost shocks) as further determinants of firms’ export behavior. Eaton, Kortum and Sotelo(2013) show that a standard heterogeneous-firm trade model with an integer number (ratherthan a continuum) of firms can reconcile the large share of a small number of firms in globaltrade, the many zeros in bilateral trade, and the observed trade volumes in cross-country data.These papers stick to homothetic preferences, hence arbitrage cannot arise. This is different fromour paper where non-homotheticities and arbitrage incentives play a central role and may per segenerate a trade participation margin.

The remainder of the paper is organized as follows. In the next section, we present the basicassumptions and discuss the autarky equilibrium. In Section 3, we use our basic framework tostudy trade patterns and trade gains in a two-country setting. Section 4 extends the analysisto many rich and poor countries. In Section 5, we introduce general preferences and showthat arbitrage equilibria also arise when consumption responds both along the extensive andthe intensive margin. Section 6 presents reduced form evidence on the association betweenUS export probabilities and a destination’s per capita income. In section 7 we show that astandard calibrated trade model (that ignores arbitrage) generates predictions on relative pricesthat violate no-arbitrage constraints in many bilateral trade relations. Section 8 concludes.

2 Autarky

We start by presenting the autarky equilibrium. The economy is populated by P identicalhouseholds. Each household is endowed with L units of labor, the only production factor.Labor is perfectly mobile within countries and immobile across countries. The labor market iscompetitive and the wage is W. Production requires a fixed labor input F to set up a new firmand a variable labor input 1/a to produce one unit of output, the same for all firms. Producinggood j in quantity q(j) thus requires a total labor input of F + q (j) /a.

Consumers. Households spend their income on a continuum of differentiated goods. Weassume that goods are indivisible and a given product j yields positive utility only for the firstunit and zero utility for any additional units.6 Thus consumption is a binary choice: either youbuy or you don’t buy. Let x(j) denote an indicator that takes value 1 if good j is purchased and

6Preferences of this type were used, inter alia, by Murphy, Shleifer and Vishny (1989) to study demandcomposition and technology choices, by Matsuyama (2000) to explore non-homotheticities in Ricardian trade,and by Falkinger (1994) and Foellmi and Zweimüller (2006) to analyze inequality and growth.

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value 0 if not. Then utility takes the simple form

U =

∫ ∞0

x(j)dj, where x(j) ∈ {0, 1} . (1)

Notice that utility is additively separable and that the various goods enter symmetrically. Hencethe household’s utility is given by the number of consumed goods.

Consider a household with income y who chooses among (a measure of) N goods supplied atprices {p(j)}.7 The problem is to choose {x(j)} to maximize the objective function (1) subjectto the budget constraint

∫ N0 p(j)x(j)dj = y. Denoting λ as the household’s marginal utility of

income, the first order condition can be written as

x(j) = 1 if 1 ≥ λp (j)

x(j) = 0 if 1 < λp (j) .

Rewriting this condition as 1/λ ≥ p (j) yields the simple rule that the household will purchasegood j if its willingness to pay 1/λ does not fall short of the price p(j).8 The resulting demandcurve, depicted in Figure 1, is a step function which coincides with the vertical axis for p(j) > 1/λ

and equals unity for prices p(j) ≤ 1/λ.

F igure 1

By symmetry, the household’s willingness to pay is the same for all goods and equal to theinverse of λ, which itself is determined by the household’s income and product prices. Intuitively,the demand curve shifts up when the income of the consumer increases (λ falls) and shifts downwhen the price level of all other goods increases (λ rises).

It is interesting to note the difference between consumption choices under these “0-1” prefer-ences and the standard CES-case. With 0-1 preferences, the household chooses how many goodsto buy, while there is no choice about the consumed quantity.9 In contrast, a household has achoice with CES preferences about the quantities of the supplied goods, but finds it optimal toconsume all varieties in positive amounts. This is because Inada conditions imply an infinitereservation price. In other words, 0-1 preferences shift the focus to the extensive margin of con-sumption, while CES preferences focus entirely on the intensive margin. It is important to note,however, that our central results below do not depend on the 0-1 assumption. In fact, we willshow below that more general preferences – which allow for both the extensive and the intensive

7Notice that the integral in (1) runs from zero to infinity. While preferences are defined over an infinitely largemeasure of potential goods, the number of goods actually supplied is limited by firm entry, i.e. only a subset ofpotentially producible goods can be purchased at a finite price.

8Strictly speaking, the condition 1 ≥ λp(j) is necessary but not sufficient for c(j) = 1 and the condition1 < λp(j) is sufficient but not necessary for c(j) = 0. This is because purchasing all goods for which 1 = λp(j)may not be feasible given the consumer’s budget. For when N different goods are supplied at the same price pbut y < pN the consumer randomly selects which particular good will be purchased or not purchased. This case,however, never emerges in the general equilibrium.

9The discussion here rules out the case where incomes could be larger than pN , meaning that the consumeris subject to rationing (i.e. he would want to purchase more goods than are actually available at the availableprices). While this could be a problem in principle, it will never occur in equilibrium.

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margin of consumption – generate results that are qualitatively similar to those derived in the0-1 case.

Equilibrium. Since both firms and households are identical, the equilibrium is symmetric.Similar to the standard monopolistic competition model, the information on other firms’ pricesis summarized in the shadow price λ. Hence, the pricing decision of a monopolistic firm dependsonly on λ. Moreover, the value of λ is unaffected by the firm’s own price because a single firmis of measure zero.

Lemma 1 There is a single price p = 1/λ in all markets and all goods are purchased by allconsumers.

Proof. Aggregate demand for good j is a function of λ only. Consequently, the pricingdecision of a monopolistic firm depends on the value of λ and not directly on the prices set bycompetitors in other markets. Thus, it is profit maximising to set p(j) = 1/λ as long as 1/λ

exceeds marginal costs. To prove the second part of the Lemma, assume to the contrary thatonly a fraction ν of consumers purchases the product at price p(j) = p = 1/λ. However, thiscannot be an equilibrium, as the firm could undercut the price slightly and sell to all consumers.

Each monopolistic firm faces a demand curve as depicted in Figure 1. It will charge a priceequal to the representative consumer’s willingness to pay p = 1/λ and sell output of quantity 1 toeach of the P households. Without loss of generality, we choose labor as the numéraire, W = 1.Two conditions characterize the autarky equilibrium. The first is the zero-profit condition,ensuring that operating profits cover the entry costs but do not exceed them to deter furtherentry. Entry costs are FW = F and operating profits are [p−W/a]P = [p− 1/a]P. The zero-profit condition can be written as p = (aF + P) /aP. This implies a mark-up µ – a ratio of priceover marginal cost – equal to

µ =aF + PP

.

Notice that technology parameters a and F and the market size parameter P determine the mark-up.10 We will show below that the mark-up is a crucial channel through which non-homotheticpreferences affect patterns of trade and the international division of labor.

The second equilibrium condition is a resource constraint ensuring that there is full employ-ment PL = FN + PN/a. From this latter equation, equilibrium product diversity (both inproduction and consumption) in the decentralized equilibrium is given by

N =aP

aF + PL.

10Notice that the determination of mark-ups is quite different between the 0-1 outcome and the standardCES-case. With 0-1 preferences, the mark-up depends on technology and market size parameters. With CESpreferences, the mark-up is determined by the elasticity of substitution between differentiated goods, while it isindependent of technology and market size. Notice further that, from the zero profit condition of the CES-model,we have ωF = (p− ω/b)xP (where x is the – endogenously determined – quantity of the representative productand 1/b is the unit labor requirement). Thus we can write the mark-up as (b/x)(F/P) + 1, which compares toa(F/P) + 1 in the 0-1 case. To achieve realistic mark-ups in empirical applications, the parameter a needs to benormalized appropriately, i.e. it has to assume an order of magnitude similar to the ratio b/x in the CES-model.

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3 Trade between a rich and a poor country

Let us now consider a world economy where a rich and a poor country trade with each other.We denote variables of the rich country with superscript R and those of the poor country withsuperscript P . To highlight the relative importance of differences in per capita incomes andpopulation sizes, we let the two countries differ along both dimensions, hence LR > LP andPR R PP . We assume trade is costly and of the standard iceberg type: for each unit sold to aparticular destination, τ > 1 units have to be shipped and τ − 1 units are lost during transport.

3.1 Full trade equilibrium

When the income gap between the two countries is small, all goods are traded internationally.In such a full trade equilibrium, a firm’s optimal price for a differentiated product in countryi = R,P equals the households’ willingnesses to pay (see Figure 1), hence we have pR = 1/λR

and pP = 1/λP . Since country R is wealthier than country P , we have λR < λP and pR > pP .By symmetry, the prices of imported and home-produced goods are identical within each country.

Solving for the full trade equilibrium is straightforward. Consider the resource constraint inthe rich country. NRF labor units are needed for setting up the NR firms. Moreover, NRPR/aand NRPP τ/a labor units are employed in production to serve the home and the foreign market,respectively. Since each of the PR households supplies LR units of labor inelastically, the resourceconstraint is PRLR = NRF + NR

(PR + τPP

)/a. Similarly, for the poor country. Solving for

N i (i = R,P ) lets us determine the number of active firms in the two countries

N i =aP i

aF + (P i + τP−i)Li, (2)

(where −i = P if i = R and vice versa).Now consider the zero-profit conditions in the two countries. An internationally active firm

from country i generates total revenues equal to pRPR+pPPP and has total costsW i[F + (P i + τP−i)/a

].

Using the zero-profit conditions of the two countries lets us calculate relative wages

ω ≡ WP

WR=aF + τPP + PR

aF + PP + τPR. (3)

When the two countries differ in population size, wages (per efficiency unit of labor) are higherin the larger country.11 Why are wages higher in larger countries? The reason is that laboris more productive in a larger country. To see this, consider the amount of labor needed by afirm in country i to serve the world market. When country R is larger than country P , firmsin country R need less labor to serve the world market because there are less iceberg lossesduring transportation, which is reflected in relative wages. There are two cases in which wagesare equalized: (i) τ = 1. When there are no trade costs, the productivity effect of country size

11While ω measures relative wages per efficiency unit of labor, ωLP /LR measures relative nominal per capitaincomes. In principle, ωLP /LR > 1 is possible, so that country P (with the lower labor endowment) has thehigher per capita income. We show below that this can happen only in a full trade equilibrium but not in anarbitrage equilibrium. The latter case is the interesting one in the present context.

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vanishes. (ii) PP = PR. When the two countries are of equal size, productivity differencesvanish because iceberg losses become equally large. Note further that τ−1 < ω < τ . When thepoor country becomes very large, iceberg losses as a percentage of total costs become negligible,ω → τ . Similarly, when the rich country becomes large, ω → τ−1.

Finally, let us calculate prices and mark-ups in the respective export destination. The budgetconstraint of a household in country i is W iLi = pi

(NR +NP

). Combining the zero-profit

condition with these budget restrictions and the above equation for the number of firms, lets usexpress the price in country i as

pi = W iLiaF + PR + τPP

aPRLR + aωPPLP, i = R,P. (4)

By symmetry, prices for the various goods are identical within each country, irrespective ofwhether they are produced at home or abroad. Consequently, imported goods generate a lowermark-up than locally produced goods because exporters cannot pass trade costs through toconsumers.12 Marginal costs are W i/a when the product is sold in the home market and τW i/a

when the product is sold in the foreign market. Hence mark-ups (prices over marginal costs) areµiD = pia/W i in the domestic market and µiX = pja/(W iτ) in the export market. Hence a fulltrade equilibrium is characterized as follows: (i) NP /NR = ωPPLP /

(PRLR

), i.e. differences in

aggregate GDP lead to proportional differences in produced varieties; (ii) pP /pR = ωLP /LR, i.e.differences in per capita incomes generate proportional differences in prices; and (iii) µPD/µ

RD =

µPX/µRX = LP /LR < 1, i.e. differences in per capita endowments lead to proportional differences

in mark-ups.

Patterns of international trade. Let us highlight how the volume and structure of interna-tional trade depend on relative per capita endowments LP /LR. We define “trade intensity” φ asthe ratio between the value of world trade and world GDP. In a full trade equilibrium the valueof world trade is given by pRNPPR + pPNRPP while world income is LRPR + ωLPPR. Tradeintensity is given by

φ =2LRPR · ωLPPP

(LRPR + ωLPPP )2

When all goods are traded, the relative size of aggregate GDP matters for trade intensity. WhenGDP differs strongly across the two countries, trade intensity is small as most world productiontakes place in the large country and most of this production is also consumed in this country.Trade intensity is maximized when the two countries are of exactly equal size. We can now statethe following proposition

Proposition 1 Assume the two countries are in a full trade equilibrium. a) All goods are traded.b) Trade intensity φ increases with both the per capita endowment LP and population size PP

if ωLPPP < LRPR. c) The impact on φ of PP is stronger than the one of LP . d) A tradeliberalization increases trade intensity if ωLPPP < LRPR.

12This is different from CES preferences, where transportation costs are more than passed through to pricesas exporters charge a fixed mark-up on marginal costs (including transportation). Notice that limited cost pass-through has been documented in a large body of empirical evidence.

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Proof. See Appendix A.

Trade and welfare. Let us finally consider the gains from trade and the welfare effects of atrade liberalization in a full trade equilibrium. Since all firms sell to all households worldwide,consumption and welfare levels are equalized across rich and poor countries. Gains from tradeare higher for the country with lower product variety under autarky. Product variety in autarkyis N i = aP iLi/

(aF + P i

). The country with a smaller population P i and/or lower per capita

endowment (lower Li) gains more from trade. Here we are interested in how bilateral tradeliberalizations affect welfare and the distribution of trade gains between the two countries. Atrade liberalization is modeled as a reduction in iceberg transportation costs τ .

In a full trade equilibrium, households in both countries purchase all goods produced world-wide. Hence the welfare levels are identical in both countries despite their unequal endowmentwith productive resources

UR = UP =aLRPR

aF + PR + τPP+

aωLPPP

aF + PR + τPP.

Firms’ price setting behavior drives this result. R-consumers are willing to pay higher pricesthan P -consumers because their income is higher. In the full trade equilibrium, higher nominalincomes translate one-to-one into higher prices, welfare is therefore identical. To see the mecha-nism by which welfare is equalized, consider mark-ups in the special case when the two countriesare equally large. When PP = PR, prices are higher in country R, while costs are the same foreach country. In other words, country-R households bear a larger share of total costs. In thiscase, the poor country’s welfare is lower under autarky.13 We summarize this in the followingproposition.

Proposition 2 In a full trade equilibrium, welfare levels are equalized. A trade liberalization (alower τ) increases welfare for both countries.

Proof. In text.

3.2 “Arbitrage“ equilibrium with non-traded goods

Full trade ceases to be an equilibrium when per capita income differences ωLP /LR become large.The reason is a threat of arbitrage. Consider a US firm that sells its product both in the USand in China. Suppose the firm charges a price in China that equals the Chinese households’willingness to pay pP = 1/λP and a price in the US that equals the US households’ willingnessto pay pR = 1/λR. If the difference between 1/λP and 1/λR is large, arbitrage opportunitiesemerge. Arbitrageurs can purchase the good cheaply on the Chinese market, ship it back to theUS, and underbid the producer on the US market. A threat of arbitrage also concerns Chinesefirms which both produce for the local market and export to the US. When these firm charge

13This continues to hold as long as PP is not too much larger larger than PR. When PP � PR, so thatωLP > LR, prices become higher in country P . In that case, country-P bears the larger share in total costs.

11

too high prices in the US, arbitrage traders purchase the cheap products in China and parallelexport them to the US.

Firms anticipate this arbitrage opportunity and adjust their pricing behavior accordingly.Notice that the threat of parallel trade only contains firms operating on the world market.Firms that abstain from selling the product in the poor country and focus exclusively on themarket of the rich country do not face such a threat. Adopting this latter strategy implies asmaller market but lets firms exploit the rich households’ high willingness to pay. In equilibrium,firms are indifferent between the two strategies. Notice that concentrating sales exclusively onthe rich market country is, in principle, an option both for producers in the rich and in the poorcountry. In equilibrium, however, only by rich-country producers adopt this strategy. While totalrevenues are independent of the producer’s location, total costs are not. To serve householdsin the rich country, country-R producers face marginal costs WRa, while country-P exportersface marginal costs WRωτ/a (they have to bear transportation costs). Since ωτ > 1, country-P producers have a competitive disadvantage in serving the rich country even when the poorcountry has lower wages ω < 1.

An arbitrage equilibrium looks as follows. A subset of rich-country producers sells theirproduct exclusively in the rich country, while the remaining rich-country producers sell theirproduct both in the rich and in the poor country. All poor-country producers sell their productworldwide. To see why this is an equilibrium, consider the alternative situation in which all rich-country producers trade their products internationally. If all firms charged a price that preventsarbitrage, all goods would be priced below rich households’ willingness to pay. In that case,however, rich households do not spend all their income, generating an infinitely large willingnessto pay for additional products. This would induce country-R firms to sell their product only onthe home market. Thus, in equilibrium, both types of firms will exist. Notice that all firms areex-ante identical (i.e. all firms have the same cost- and demand functions). Notice that there isan indeterminacy concerning the selection of firms into export status. Clearly, this is an artefactof the symmetry-assumption, which would disappear once asymmetries (i.e. firm heterogeneities)are added to the model.

We are now ready to solve for the arbitrage equilibrium. Denote the price in the rich countryof traded and non-traded goods by pRT and pRN , respectively. The price of non-traded goods ispRN = 1/λR. Anticipating the threat of parallel trade, the price of traded goods may not exceedand exactly equals the price in the poor country (plus trade costs), pRT = τ/λP , in equilibrium.The price of a product in the poor country is still given by pP = 1/λP . The following lemmaproves that this is a Nash equilibrium.

Lemma 2 In an arbitrage equilibrium, firms that sell their product in both countries (i) setpP = 1/λP in country P and pRT = τpP in country R, and (ii) sell to all households in bothcountries.

Proof. (i) Assume 1/λP exceeds marginal costs of exporting. In that case, the profitmaximization problem of an exporting firm reduces to maximize total revenue PP pP (j)+PRpR(j)

s.t. τpP (j) ≥ pR(j) and pi(j) ≤ 1/λi. Applying Lemma 1, it is profit maximizing to set

12

pi(j) = 1/λi if τ/λP ≥ λR (full trade equilibrium). If τ/λP < λR, the arbitrage constraint isbinding τpP (j) = pR(j) = pRT and revenues are maximized when pP (j) = 1/λP . (ii) Assume tothe contrary that only a fraction ν of consumers purchases the product at price pP (j) = 1/λP .As in Lemma 1, this cannot be an equilibrium, as the firm would lower pP (j) and pR(j) slightlyand gain the whole market in the poor country.

The zero-profit condition for an internationally active country-i producer is pRTPR+pPPP =

W i[F + (P i + τP−i)/a

]. These firms’ total revenues do not depend on the location of produc-

tion, but the required labor input depends on location. Differences in population sizes generatedifferences in (total) transport costs, and relative wages equalize these differences. From thezero-profit conditions we see that relative wages ω are still given by equation (3). The zero-profitconditions also let us derive the prices for the various products. Using pRT = τpP , we get

pRT =τ

a

aF + PR + τPP

τPR + PPand pP =

1

a

aF + PR + τPP

τPR + PP,

where we have set WR = 1. (We use this normalization throughout the paper.) The zero-profitcondition for an exclusive rich-country producer is pRNPR = F +PR/a, from which we calculatethe equilibrium price of a non-traded variety

pRN =aF + PR

aPR.

Notice that, due to the arbitrage constraint on exporters’ pricing behavior, prices do not dependon LP and LR. This is quite different from the full-trade equilibrium, where price differencesreflect differences in per capita endowments.

The resource constraint in country P is the same as that in the full trade equilibrium, soNP is still given by (2). The resource constraint in country R is now different, however, becausethere are traded and non-traded products. Denoting the range of traded and non-traded goodsproduced in the rich country by NR

T and NRN , respectively, the resource constraint of country

R is given by PRLR = NRT

(F + (PR + τPP )/a

)+ NR

N

(F + PR/a

). Together with the trade

balance condition NRT p

PPP = NP pRTPR and the terms of trade pRT /pP = τ we get

NRT =

aPR

aF + τPR + PPτLP , and NR

N =aPR

aF + PR(LR − τωLP

). (5)

Patterns of international trade. Let us now describe volume and structure of internationaltrade in an arbitrage equilibrium. The value of traded goods is pRTN

PPR+pPNRT PP (while world

income still is LRPR +ωLPPR). Using equations (2) and (5) we calculate the trade intensity inan arbitrage equilibrium.

φ =2τ

τ + (PP /PR)· ωLPPP

LRPR + ωLPPP(6)

Equation (6) shows that per capita incomes differences and differences in population sizes affecttrade intensity in different ways. Consider first the impact of a given change in per capita

13

income of country P . The above expression for φ reveals that a higher per capita income of thepoor country unambiguously increases the intensity of trade. This is reminiscent of the Linder-hypothesis (Linder 1961) postulating that a higher similarity in per capita incomes is associatedhigher trade between trading partners. The intuition for this result is straightforward. When LP

increases by 10 percent, the range of exported goods increases by 10 percent while prices remainunchanged. Hence the aggregate value of trade pRTN

PPR + pPNRT PP increases by 10 percent

as well. In contrast, increasing LP by 10 percent (while leaving LR unchanged) increases worldGDP by less than 10 percent. Trade intensity, the ratio between world trade and world GDP,thus rises unambiguously.

Now consider a change in population-size of country P . It turns out that a change in PP hasa smaller effect on trade intensity than an increase in relative per capita incomes that increasesGDP by the same magnitude, i.e. we have ∂logφ/∂ logPP < ∂ log φ/∂ logLP . This can be seenfrom looking at the volume of world trade which is equal to 2pPNR

T PP . An increase in PP hasa direct and an indirect effect on world trade. The direct effect increases trade in proportion tocountry P ’s population. The indirect effect lowers per capita imports. Notice that imports percapita in country-P are equal to pPNR

T =[τ/(τ + PP /PR)

]ωLP . From the point of view of

country R, a larger population in country P requires fewer exports to each country-P householdsto cover a given amount of own imports. Hence country-P imports (and world trade) increasewith PP less than proportionately.14

Proposition 3 Assume per capita income differences are large, so that the world economy is inan arbitrage equilibrium. a) Some firms in country R do not export. b) An increase in per capitaendowment LP raises trade intensity φ, while an increase in population size PP may increase ordecrease φ. c) The impact on φ of PP is weaker than the one of LP . d) A trade liberalizationdecreases trade intensity.

Proof. See Appendix B.

Trade and welfare. We proceed by looking at the impact of trade liberalizations. We firstconsider the case where trade costs are symmetric and explore a bilateral liberalization. (Welook at the unilateral case below). In an arbitrage equilibrium, a bilateral trade liberalizationlets consumers’ welfare levels in the two countries diverge. Country-P households’ welfare equalsNRT + NP , while country-R households’ welfare equals NP + NR

T + NRN . Using (2) and (5),

these welfare levels are given by

UP =aLP (PP + τPR)

aF + τPR + PPand UR =

aLP (PP + τPR)

aF + τPR + PP+aPR

(LR − τLP

)aF + PR

.

It is straightforward to verify, that ∂UP /∂τ > 0 while ∂UR/∂τ < 0. We are now able to statethe following proposition.

14Notice that an increase in PP also increases ω. It is shown in the proof of proposition 2 (see Appendix) thattaking the impact of PP on ω into account, an increase in PP still reduces per capita imports.

14

Proposition 4 In an arbitrage equilibrium, a trade liberalization increases the welfare of country-R households, but decreases it for country-P households.

Proof. In text.

Proposition 4 shows the crucial role of trade costs for welfare. Unequal countries have differentpreferred trade barriers (or different preferred degrees of trade liberalizations). Consumers inthe rich country are essentially free-traders, whereas consumers in the poor country are harmedby liberalizations. What is the intuition behind this result? The reason is country-R firms’pricing behavior. As higher trade costs imply a less tight arbitrage constraint, country-R firmscan charge higher prices for traded goods relative to non-traded goods. This induces country-Rfirms to export rather than sell exclusively to domestic customers. The result is an increase intrade intensity which benefits the poor country. Put differently, poor country households areagainst a trade liberalization because a lower τ decreases trade and welfare in country P .

Unilateral trade liberalization. Up to now we have assumed symmetric trade costs acrosscountries. However, policy makers can influence trade costs through tariffs and regulations. Thisis interesting in the present context because, in an arbitrage equilibrium, the poor country hasan incentive to increase trade barriers and relax the arbitrage constraint. This increases thesupply of northern varieties and hence may raise welfare in the South. It is therefore interestingto look at an unilateral trade liberalization. Assume that trade costs differ between countries,with τ i denoting iceberg costs for imports into country i. While total revenues of exporters arestill pRTPR + pPPP , now total costs do not only vary as a result of unequally large populationsbut also because of differences in transportation costs, W i

[F + (P i + τ−iP−i)/a

]. From the

zero-profit condition we derive relative wages ω as

ω ≡ WP

WR=aF + τPPP + PR

aF + PP + τRPR,

which implies that(τR)−1

< ω < τP . Assume that income differences are sufficiently large,ωLP /LR < τR, so that an arbitrage equilibrium prevails. To prevent arbitrage, the price oftraded goods in the rich country may not exceed the price in the poor country plus transportationcosts, hence firms will charge pRT = τRpP in the rich country.15

Using zero-profit conditions and resource constraints is it is straightforward to calculatewelfare in the two countries as

UP =aPP + aτRPR

aF + τRPR + PPLP and UR = UP +

aPR

aF + PR(LR − τRωLP

).

Interestingly, a unilateral trade liberalization by the poor country (a fall in τP ) does not haveany effect on poor households, but affects rich households through a fall in ω. Lower costs ofexporting to the poor country makes producers in country R more productive, improving their

15To make sure that such an equilibrium exists, we also assume that country-R exporters can charge a price incountry P that covers (production plus transportation) costs, pP > τP /a. This implies τP τR < aF/PR + 1. Ifthis condition is satisfied also country-P exporters will export, pRT > τR/a because pRT = τRpP .

15

terms of trade while leaving the arbitrage constraint unaffected. This saves resources for countryR which are employed to produce non-traded goods. This raises welfare of rich consumers.In contrast, an unilateral increase in trade barriers into the rich country (a larger τR) harmscountry-R but benefits country-P households. Hence, our model predicts that a poor countryhas an incentive to levy an export tax. This relaxes the arbitrage constraint and increases thesupplied varieties and hence welfare in country P .

3.3 Existence of equilibria

The conditions under which the threat of parallel trade becomes binding and the economyswitches from a full trade to a partial trade equilibrium are straightforward. In a full tradeequilibrium, relative prices equal relative per capita incomes pP /pR = ωLP /LR. In that case,differences in willingnesses to pay must be small enough, λP /λR ≤ τ , so that the threat ofparallel trade is not binding. In contrast, when differences in willingnesses to pay become large,λP /λR > τ , the parallel trade constraint kicks in. This happens when

ωLP

LR> τ−1. (7)

In other words, a full trade equilibrium emerges when per capita incomes are similar, while anarbitrage equilibrium emerges when the gap in per capita incomes is large.

Up to now we have implicitly assumed that trade costs are sufficiently low so that the twocountries will engage in trade. The following proposition proves existence of a general equilibriumwith trade.

Proposition 5 When τ ≤ τ∗ ≡√aF/PR + 1, the two countries will trade with each other for

all LP /LR ∈ (0, 1].

Proof. See Appendix C.

The trade condition in the proposition makes sure prices in country P are sufficiently highto induce country-R firms to export their product. Notice that, with τ ≤ τ∗, country-P firmsare also willing to export since they can charge a price pRT > pP < τ/a. The trade condition isquite intuitive. Trade is more valuable when fixed costs are high, as these costs are spread outover a larger market. For the same reason, trade is more valuable if the local market is small.Hence the critical value of iceberg costs τ∗ is increasing in F and falling in PR. Notice alsothat the trade condition makes a statement about the relative size of trade costs and the squareroot of the mark-up. One could argue that empirically observed mark-ups are often lower thanobserved trade costs, thus contradicting the trade condition. Notice, however, that aF/PR+1 isthe mark-up of a (northern) firm that sells its product exclusively on the home market, while theaverage mark-up in the economy is a weighted average of these non-exporting firms (with highmark-ups) and exporting firms (with low mark-ups). Hence, our simple model can accommodatea situation where there is trade, even though the economy-wide mark-up falls short of tradecosts.

16

Figure 2 shows the relevant equilibria in (LP /LR, τ) space. There is full trade in region Fwhich emerges at high values of LP /LR and intermediate values of τ . An arbitrage equilibriumprevails in region A which arises at low trade costs and high income differences. Figure 2 alsoshows what happens when population size in the poor country increases. In that case, thedownward-sloping branch that separates regions F and A shifts to the left. When the poorcountry is larger, τ∗ is unaffected and there are more parameter constellations (LP /LR, τ) underwhich a full trade equilibrium emerges. In this sense, a larger population in the poor countryfosters trade.16

Figure 2

Figure 3 shows the welfare responses of changes in τ across the various regimes graphically.Panel a) is drawn for relatively low per capita income differences ωLP /LR > τ∗. In that case, anarbitrage equilibrium emerges with low trade costs, while a full trade equilibrium emerges withmoderate trade costs. Panel b) is drawn for higher per capita income differences ωLP /LR ≤ τ∗ sothat a full trade equilibrium is not feasible. Country-R welfare (the bold graph) is monotonicallydecreasing in τ in both panels of Figure 3. Hence the R-consumer reaches his maximum welfarewhen trade costs are at their lowest possible level τ = 1. In contrast, the impact of τ on country-P welfare (the dotted graph) interacts with per capita income differences. When these differencesare low (panel a), country-P welfare increases in τ when τ <

(ωLP /LR

)−1 and decreases in τwhen τ ≥

(ωLP /LR

)−1. Welfare is maximized at τ =(ωLP /LR

)−1 (when the equilibriumswitches from a full-trade to an arbitrage equilibrium). When per capita income differences arelarge (panel b), country-P welfare decreases monotonically in τ (full trade is not feasible) andwelfare is maximized at τ = τ∗.

Figure 3

4 Many rich and poor countries

In an arbitrage equilibrium with two countries, all firms in the poor country are exporters whileonly a subset of firms in the rich country exports. Moreover, a trade liberalization that relaxesthe arbitrage constraint always hurts poor consumers. We now show that these predictions needto be qualified in a multi-country world. The effect of moving from two to many countries canbe most easily shown when there are n identical rich countries and m identical poor countries,i.e. a world with a fragmented rich North and a fragmented poor South. As before, we assumethat countries differ in per capita endowments (and population size) but are identical in all otherrespects.

The general equilibrium has a structure very similar to that of the two-country case. From thezero-profit conditions for internationally active firms, it is straightforward to show that relative

16Notice that there is international trade even when income differences become extremely large and LP /LR

becomes very small. The range of traded goods approaches zero, however, when LP /LR goes to zero.

17

wages are now given by

ω ≡ WR

WP=aF + τP−R + PR

aF + τP−P + PP,

where P−R = (n−1)PR+mPP and P−P = nPR+(m−1)PP are rest-of-the-world populationsfrom the perspective of country R and country P , respectively. In full world trade equilibrium,relative prices of southern relative to northern markets are determined by relative per capita in-comes, pP /pR = ωLP /LR, and the ratio of produced varieties still reflects differences in aggregateGDP, NP /NR = ωLPPP /LRPR.

The interesting case is when income differences are sufficiently large, so that ωLP /LR > τ−1.In that case, the arbitrage constraint is binding, limiting trade between the rich North and thepoor South. A northern firm now has two options: either export worldwide or export only toother northern countries. Notice that, unlike in the two-country case, all northern firms are nowexporters. Firms that export exclusively to the North have a smaller market but can chargehigher prices. Firms that export to all countries worldwide set low prices but have the largeworld market. While large differences in per capita incomes limit trade across regions, there isfull trade within regions. As there are no income differences within a region, all goods producedin that region are also sold to other countries in that region.

The arbitrage equilibrium can now be solved in a straightforward way (for details see Ap-pendix E). We first study how differences in per capita incomes and population sizes affect tradeintensity. It is straightforward to calculate

φ = 2mωLPPP

nLRPR +mωLPPP(m− 1)PP + τPR

mPP + nτPR+ 2

(n− 1)LRPR

nLRPR +mωLPPP.

which readily reduces to the expression derived in the last section when n = m = 1. An increasein LP increases world trade intensity (and reduces North-North trade with exclusive goods). Itcan also be shown that a larger population in the South has a weaker effect on trade intensitythan a larger per capita income. Hence with respect to per capita incomes and populations sizes,the results of the two-country case carry over to the multi-country framework.

In contrast to the two-country case, the effect of a trade liberalization on welfare is nowambiguous. There are two effects. On the one hand, a lower τ implies a tighter arbitrageconstraint for globally active producers. Lower prices for globally traded products (relativeto products exclusively sold in the North) induce former northern world-market producers toconcentrate their sales on northern markets only. This reduces trade intensity between theNorth and the South. On the other hand, a reduction in τ stimulates trade within regions.While South-South trade increases less than North-South trade falls (first term of above equationincreases in τ), North-North trade unambiguously increases (second term decreases in τ). A tradeliberalization is more likely to stimulate trade if there are more countries with a region. Within-regional trade is more strongly affected in this case and dominates the reduction in North-Southtrade. A trade liberalization is also more likely to stimulate North-South trade, the larger isthe North relative to the South. In that case, North-North trade (which is positively affected)comprises the bulk of world trade. When the North is much larger than the South, positive

18

effects on North-North trade of a trade liberalization dominate negative effects on North-Southtrade flows.

It turns out that the welfare level of a country-P household is given by

UP = mNP + nNRN =

aLP (mPP + τnPR)

aF + τP−P + PP.

It is straightforward to see that ∂UP /∂τ < 0 if aF < (m − 1)PP (1 + (m/n) (PP /PR)). Thismeans that a trade liberalization may raise welfare in country P and is more likely to do so thehigher is mPP . A reduction in τ has two opposing effects. The arbitrage channel is still at workand induces northern firms to abstain from selling to southern households. This is harmful forsouthern welfare. However, a lower τ stimulates South-South trade, which has a beneficial effecton southern welfare. Households in the poor country gain from a trade liberalization when thereare many poor countries and when poor countries are large. In such a situation, there is a lotto gain from South-South trade because there are many trade barriers and because the southernmarkets are large.

We summarize the above discussion in the following

Proposition 6 Assume there are m identical poor countries and n identical rich countries,with LP /LR < (ωτ)−1. a) All northern firms export, but some of them export only to othernorthern countries; b) A trade liberalization (a lower τ) unambiguously increases welfare of richhouseholds. It increases welfare of poor households if aF < (m−1)PP (1 + (m/n) (PP /PR)) anddecreases it otherwise. The increase in welfare is larger in the North than in the South.

Proof. In text.

Notice that the multi-country model generates an empirically testable hypothesis. The modelpredicts a positive correlation between the export probability of a northern firm and the percapita income of a potential destination. In our simple model, the probability that a firm froma rich country exports to another rich country is 100 percent. (The prediction that 100 percentof all firms export is clearly an artefact arising from the assumed absence of firm heterogeneity.)In contrast, the probability that a northern firms exports to a poor country is less than 100percent and is lower the poorer a potential destination. Below, we will test this prediction byinvestigating whether and to which extent US export probabilities of HS6-digit product categoriesare indeed positively related to potential destinations’ per capita incomes.

5 General preferences

The assumption of 0-1 preferences yields a tractable framework with closed-form solutions. How-ever, the focus is entirely on the extensive margin of consumption. This contrasts with thestandard CES case where all adjustments happen along the intensive margin. We go beyondthese two polar cases in this section by studying general preferences. We show that the qual-itative characteristics of the equilibria under 0-1 preferences carry over to general preferences

19

featuring non-trivial intensive and extensive margins of consumption.17 In particular, we pre-cisely define the conditions under which an arbitrage equilibrium with non-traded goods existsand also provide a simple calibration exercise showing that arbitrage equilibria emerge underreasonable parameter values and that there is a quantitatively strong relationship between percapita incomes on the extensive margin of trade.

5.1 Utility and prices

Let us go back to the setup of Section 3 with two countries that differ in per capita income andpopulation size. However, let household welfare take the general form

U =

∫ ∞0

v(c(j))dj, (8)

where c(j) denotes the consumed quantity of good j. It is assumed that the subutility v()

satisfies v′ > 0, v′′ < 0 and v(0) = 0. Beyond these standard assumptions, we make two furtherassumptions on the function v(): (i) v′(0) < ∞, (ii) v′′(0) > −∞, and (iii) −v′(c)/[v′′(c)c]is decreasing in c. The first assumption implies that reservation prices are finite, generating anon-trivial extensive margin of consumption; the second ensures that an arbitrage equilibriumexists when per capita income differences are sufficiently high (see below); and the third impliesa price elasticity of demand decreasing along the demand curve. Monopolistic pricing leadsto p = (1 + v′′(c)c/v′(c))−1b, where b denotes marginal cost. To simplify notation, we denotethe mark-up by µ(c) ≡ (1 + v′′(c)c/v′(c))−1. Assumptions (i)-(iii) imply that µ(0) = 1 andµ′(c) > 0.18

How does firms’ price setting behavior change when there are consumer responses along theintensive margin? With 0-1 preferences, the monopoly price equals the representative household’swillingness to pay and does not depend on marginal production costs. With general preferences,however, firms solve the standard profit maximization problem: the price equals marginal coststimes a mark-up that depends on the price elasticity of demand. This implies an important differ-ence to the case of 0-1 preferences. With general preferences, there are price differences betweenimported and domestically produced goods. While symmetric utility implies that importers andlocal producers within a given location face the same demand curve, marginal costs differ sinceimporters have to bear transportation costs and since wages vary by location. To allow for suchdifferences, we denote by pij , c

ij and bij , respectively, the price, quantity and marginal cost of a

good produced in country j and consumed in country i. Unconstrained monopoly pricing impliespij = µ(cij)b

ij .

17Li (2012) and Bronnenberg (2015) propose other ways to study the trade-off between intensive and extensivemargins of consumption by sticking to CES preferences but allowing for fixed purchasing costs.

18µ′(c) > 0 follows directly from assumption (iii). To see why µ(0) = 1 we use l’Hopital’s rulelimc→0 v

′(c)c/v(c) = limc→0 (1 + v′′(c)c/v′(c)). However, limc→0 v′(c)c/v(c) = v′(0) · limc→0 c/v(c) =

v′(0)/v′(0) = 1. This implies limc→0 v′′(c)c/v′(c) = 0 and hence limc→0 µ(c) = 1. Since the monopolist opti-

mally chooses a price along the elastic part of the demand curve, no further restrictions on the µ(c)-function areneeded.

20

5.2 The arbitrage equilibrium

The arbitrage equilibrium features a situation in which (i) only a subset of country-R producerssell their product worldwide at sufficiently low prices to avoid arbitrage; (ii) the remainingcountry-R firms sell their product exclusively in the rich country at the unconstrained monopolyprice; (iii) all poor-country producers export their products, also at prices that avoid arbitrage.The discussion in this section focuses on the conditions under which an arbitrage equilibriumexists. (Appendix E provides the full system of equations that characterize such an equilibrium.)

The arbitrage constraints for country-R and country-P producers, respectively, are now givenby

1/τ ≤ pRR/pPR ≤ τ and 1/τ ≤ pPP /pRP ≤ τ.

A necessary condition for the existence of an arbitrage equilibrium is that these constraintsare binding, so that pRR/p

PR = pRP /p

PP = τ . This happens to be the case if the gap in per

capita incomes becomes sufficiently large. As LR/LP , and hence cRR/cPR, get large the ratio of

(unconstrained) monopoly prices eventually exceeds trade costs, or µ(cRR)/µ(cPR) > τ2. (Recallthat µ′(c) > 0.) Notice, however, that a binding arbitrage constraint does not necessarily implythat there are non-traded goods. The reason is that adjustment now does not only occur at theextensive margin but also at the intensive margin. Hence there are full trade equilibria wherethe arbitrage constraint binds.

To verify the existence of an arbitrage equilibrium with non-traded goods, we look at incen-tives of country-R firms to sell exclusively on the home market rather than selling their productsworldwide. A country-R producer’s profit is given by (to ease notation we write pRR ≡ τp andpPR ≡ p)

π = PR (τp− 1/a) cRR + PP (p− τ/a) cPR.

The corresponding demand curves are given by the first order conditions v′(cRR) = λRτp andv′(cPR) = λP p for households in country-R and and country-P , respectively. This yields dcRR/dp =

(1/p)v′(cRR)/v′′(cRR) and dcPR/dp = (1/p)v′(cPR)/v′′(cPR). The first order condition of the monopo-listic firm’s price setting choice is given by

τp− 1/a

p

(−v′(cRR)

v′′(cRR)

)+p− τ/a

p

(−v′(cPR)

v′′(cPR)

)PP

PR= τcRR + cPR

PP

PR.

To examine whether an arbitrage equilibrium exists, let LP and therefore cPR approach zero,all other exogenous variables (including PP /PR) remain fixed. The first order condition thenbecomes

τp− 1/a

τp

(−

v′(cRR)

v′′(cRR)cRR

)+p− τ/aτpcRR

(− limcPR→0

v′(cPR)

v′′(cPR)

)PP

PR= 1.

Now consider the optimal decision of a country-R firm whether to produce exclusively for thehome market. Denoting by pN and cNR price and quantity of non-traded goods, the first order

21

condition for exclusive producers is

pN − 1/a

pN

(−

v′(cNR )

v′′(cNR )cNR

)= 1.

When τ is sufficiently low, so that p > τ/a, comparing the last two equations shows that theprice of a non-exporting firm pN is strictly larger than the price of an exporting firm τp. (Thisis because, by assumption, −v′(0)/v′′(0) > 0.) Since cPR → 0 when LP → 0, export revenuesare zero. Hence non-exporters charge higher prices and their profits are larger than those ofexporters. This implies that an outcome where all firms export cannot be an equilibrium. Wesummarize our discussion in

Proposition 7 There is a critical income gap ∆ such that, for all LP /LR < ∆, an equilibriumemerges in which only a subset of goods is traded.

Proof. In text.

The above proposition implicitly assumes an equilibrium where the two countries trade witheach other. This is not a priori clear because the countries may also remain in autarky. Thefollowing proposition shows that transportation costs need to fall short of a certain limit to makesure that trade will take place in equilibrium.

Proposition 8 Denote by cRa consumption per variety under autarky in the rich country. Therewill be trade in equilibrium, if τ < µ(cRa )v′(0)/v′(cRa ) where aF/PR = cRa (µ(cRa )− 1).

Proof. See Appendix F.

An important result we derived under 0-1 preferences holds that population size has a weakereffect than per capita incomes in determining trade patterns. We now demonstrate that this isalso true with general preferences. The previous proposition showed that, starting from a fulltrade equilibrium, increasing the gap in per capita incomes will eventually generate an arbitrageequilibrium with non-traded goods. We now show this is not necessarily the case, when weincrease relative population size.

To make this point, we proceed as follows. We first observe that, starting from a full tradeequilibrium, an increase in LP /LR beyond unity eventually leads to a “reversed” arbitrage equi-librium, in which some country-P producers sell only on the domestic market while all country-Rproducers export. We now show that such a reversed arbitrage equilibrium cannot emerge froma successive increase in PP /PR (keeping LP /LR < 1 constant), because this does not generateprice differences sufficiently large to escape a full trade equilibrium. In other words, increasingPP /PR, we cannot reach a situation where both arbitrage constraints are violated, µ(cPR) ≥ µ(cRR)

and µ(cPP ) ≥ µ(cRP )τ2. To see this, consider the households’ budget constraints

aLR = NPµ(cRP )cRP τω +NRµ(cRR)cRR

aLP = NPµ(cPP )cPP +NRµ(cPR)cPRτ/ω,

22

and take the difference between the two equations. If both arbitrage conditions are violated,the budget constraints can only hold if ω > τ . However, if ω > τ the zero-profit condition isviolated in at least one country in a full trade equilibrium (where firms charge the unconstrainedmonopoly price). In such an equilibrium, the zero-profit condition in country j is given by

PRcRj (µ(cRj )− 1)/a+ PP cPj (µ(cPj )− 1)τ/a = F,

where piP > piR and ciP < ciR, since country P has higher marginal cost than country R, both onthe domestic and the export market. However, this implies ciP (µ(ciP ) − 1) < ciR(µ(ciR) − 1) forboth i = P and i = R, i.e. country R-producers make strictly larger profits on both markets. Itfollows that, when the zero-profit condition holds in country R, it must be violated in country P ,and vice versa, if country P is the low-wage country. In the latter case, we must have ω > 1/τ

to ensure that both zero-profit conditions can hold simultaneously. Hence we have ω ∈ (1/τ, τ)

in a full trade equilibrium with unconstrained price setting. In sum, we always have ω < τ

in a full trade equilibrium. But this implies that households’ budget constraints continue tohold simultaneously when PP /PR gets very large. Thus, unlike a successive increase in LP /LR

(beyond unity), it is not possible to reach a “reversed” arbitrage equilibrium with a successiveincrease in PP /PR. In this sense, the difference in population sizes has a weaker effect on tradepatterns than the difference in per capita endowments. We summarize our discussion in thefollowing

Proposition 9 Per capita endowments are more important for trade patterns than populationsizes. Starting from a full trade equilibrium with unconstrained price setting, successive increasesin LP /LR (beyond unity) lead to a “reversed” arbitrage equilibrium, while successive increases inPP /PR cannot generate a reversed arbitrage equilibrium.

Proof. In text.

6 Reduced-form empirical evidence

Before we start with a model-based approach to shed light on the empirical relevance of arbitrage,it seems useful to test the prediction (developed at the end of section 4) of a positive relationshipbetween a rich country’s export probability and a destination’s per capita income. If the arbitrageconstraint is at work, such a positive relation between the extensive margin of exports and theper capita income of a potential destination should be observed in the data.

We analyze the following empirical model

D(i, k) = α0 + α1 lnGDP (k) + α2 ln y(k) +X(i, k)β + φ(i) + e(i, k),

where D(i, k) indicates whether the US exports product i to country k, GDP (k) is aggregateGDP of country k, and y(k) denotes per capita income of country k. X(i, k) is a vector ofcontrols,19 φ(i) is a product-fixed effect, and e(i, k) is an error term.

19Control variables include: log of distance between exporter’s and importer’s capital, dummy for a common

23

We use UN Comtrade data complied by Gaulier and Zignago (2010) containing yearly uni-directed bilateral trade flows at the 6-digit-level of the Harmonized System (1992) for the year2007. We observe 5,018 product categories at the 6-digit level. We look only at consumer goods(according the BEC classification). This leaves us with 1,263 product categories from which weexclude those 11 categories the US did not export in 2007. Our data set includes 135 potentialexport destinations. Information on per capita incomes (2005 PPP-adjusted USD) and popula-tion sizes are taken from Heston et al. (2006). We exclude all bilateral trade flows with negativequantities and set D(i, k) = 0 when the observed quantity falls short of USD 2,000. We end upwith 169,020 potential export flows (1,252 products × 135 potential importers). 39.1 percent ofthese potential export flows actually materialized in 2007.

A crucial prediction of our model is α2 > 0: a destination’s per capita income is a significantdeterminant for the export probability, conditional on the destination’s aggregate GDP. In thestandard homothetic model we should have α2 = 0, since there is no extra role for a destination’sper capita income once aggregate GDP is controlled for. The estimates of Table 1, column 1,clearly indicate that α2 is positive, statistically significant, and qualitatively large: doubling adestination’s per capita income, holding its aggregate GDP constant, increases the US exportprobability of a HS6 digit product category by 8.5 percentage points. The estimates of column1 also imply that a destination’s per capita income is more important than its population size.To see this, denote by Pop(k) destination k’s population size, so that lnPop(k) = lnGDP (k)−ln y(k). This lets us rewrite the empirical model asD(i, k) = α0+(α1+α2) ln y(k)+α1 lnPop(k)+

... Hence doubling the per capita income (holding population size constant) increases the exportprobability by 14.9 (= 8.5 + 6.4) percentage points, while doubling population size (holdingper capita income constant) increases it by only 6.4 percentage points. We conclude that theempirical evidence is consistent with the predictions of our model, according to which per capitaincome play a more important role than populations size to explain the extensive margin ofinternational trade (see Propositions 3 and 9).

Table 1

To check the robustness of our estimates, columns 2-6 of Table 1 replace the regressor ln y(k)

by a set of dummy variables to allow for a more flexible impact of per capita incomes on exportprobabilities.20 In column 2, we use the same sample as in the log specification of column 1;column 3 excludes very small destination (with population size less than 1 million); and column4 and 5 aggregate export probabilities to HS4 and HS2 digit levels, respectively. Results indicate

border, dummy for importer being an island, dummy for importer being landlocked, dummy for importer andexporter ever having had colonial ties, dummy for currency union between importer and exporter, dummy forimporter and exporter sharing a common legal system, dummy for religious similarity, dummy for importer andexporter having a free trade agreement, and dummy for importer and exporter sharing a common language.

20The estimated model is D(i, k) = α0 + α1 lnGDP (k) +∑6n=1 α2nDy(k, n) +X(i, k)β + φ(i) + e(i, k), where

Dy(k, n) indicates whether of not destination k falls into per capita income category n. We classify countriesinto 7 per capita income groups: (i) lower than USD 1000; (ii) USD 1000-1999; (iii) USD 2000-3999; (iv) USD4000-7999; (v) USD 8000-15999; (vi) USD 16000-31999; and (vii) USD 32000 or larger. The group with per capitaincome larger than USD 32,000 serves as the reference group.

24

a monotonic impact of per capita income, which is robust across specifications.21

Obviously, a positive relationship between export probabilities and per capita incomes doesnot mean that only arbitrage constraints are driving the empirical evidence. Export zeros couldalso be the results of cost constraints (i.e. the marginal cost of exporting to particular desti-nation exceeds that destination’s reservation price). Standard heterogeneous-firm models canaccommodate the results of Table 1 only with additional parameters, e.g. by assuming hetero-geneous market-entry costs depending on the destination’s per capita income. Simple specifica-tions of non-homothetic preferences that have been frequently used in the earlier literature (e.g.Bergstrand 1990, Mitra and Trindade 2005) typically work with a homogenous and a differen-tiated good. Such specifications of non-homotheticities generate a bang-bang solution: eitherconsumers buy no differentiated goods or all of them. Again, additional parameters like prefer-ence heterogeneity across countries would have to be introduced to produce export zeros. Morerecent papers mentioned in the introduction combine non-homothetic preferences and supply het-erogeneities to generate non-negativity constraints so that export zeros can emerge. Clearly, theempirical evidence of Table 1 cannot discriminate between export zeros arising from a reservationprice falling short of marginal production costs; and export zeros arising from international ar-bitrage due to large per capita income differences. Therefore, in the next section, we go one stepfurther and check quantitatively whether binding arbitrage can arise in a calibrated standardmodel, thus speaking more specifically to the empirical relevance of the arbitrage channel.

7 Are no-arbitrage constraints binding in a calibrated model?

In this section, we calibrate a multi-country trade model with non-homothetic preferences. Thismodel makes predictions about prices in the various destination but rules out arbitrage byassumption. The idea is to check whether the price distribution predicted in such a modelis such that arbitrage opportunities exist. If this is the case for many exporters (and a highexport volume), we take it as evidence that points to the potential relevance of internationalarbitrage.22

Arbitrage in a multi-country framework. In a multi-country framework, arbitrage op-portunities can not only arise directly within a country pair but also indirectly through a thirdcountry. A direct arbitrage opportunity occurs through parallel-imports – when the relative pricebetween origin i and destination j exceeds trade costs τji (so that arbitrageurs can buy cheaplyin j and undercut the price in i); or through parallel-exports – when the relative price between

21In Tables A1 and A2 of the Online Appendix, we provide further robustness checks. In Table A1, we showthat US regressions for each single year 1997-2006 yield estimates very close to those obtained for the year 2007,which we report in Table 1. In Table A2 we look at the 14 largest consumer goods exporters (rather than only theUS). For all these large exporting countries we find a significant effect of destinations’ per capita income, holdingdestinations’ GDP constant (the only exception being China and Mexico where the effect is not statisticallysignificant). These results are also in line with the evidence in Baldwin and Harrigan (2011) and Bernasconi andWuergler (2012) where, respectively, output per worker and income per capita are included as control variablesin extensive margin regressions.

22We thank an anonymous referee for making this suggestion.

25

destination j and origin i exceeds trade costs τij (so that arbitrageurs can buy cheaply in i andundercut in j).

Importantly, however, in a world economy with many countries, the arbitrage channel mayalso work indirectly through third countries. Consider the example of a US firm that sells itsproduct in Korea. Korean consumers are poorer than US consumers. Therefore, the US firmwants to charge a lower price in Korea. It can do so because trade costs from Korea to the USare relatively high and as a consequence arbitrageurs do not find it profitable to ship the goodsback to the US. However, if the same US firm also serves the Chinese market, it is likely tobe indirectly constrained on the Korean market. The reason is that arbitrageurs may purchasecheaply on the Chinese market and underbid in Korea. Such a scenario is likely since incomedifferences between Korea and China are high, while trade costs are comparably low. In fact,such a constellation emerges in the numerical analysis discussed below.

The above discussion suggests the following simple rule to identify whether a producer fromcountry i is subject to (direct or indirect) arbitrage in destination j: we need to check, for allpossible country triples (i, j, k), whether the following inequality holds

pijpik

> τkj , (9)

where pij is the price charged by the producer from country i in destination j and τkj are thetrade costs from country k to country j.

Equation (9) encompasses both cases of direct and indirect arbitrage. Indirect cases arerepresented by i 6= j 6= k. Direct cases are represented by k = i 6= j (parallel exports) andi = j 6= k (parallel imports). The I − 1 countries from where a threat of arbitrage potentiallyoriginates include the I−2 third countries (indirect arbitrage) and one of the two trading partners(direct arbitrage). A threat of indirect arbitrage emerges when i 6= j 6= k (purchasing country igoods cheaply in destination k and undercutting in destination j). A threat of parallel exportsoccurs when the above inequality holds for k = i 6= j (purchasing cheaply in the home market iand underbid in destination j). A threat of parallel imports occurs when the above inequalityholds for i = j 6= k (purchasing cheaply in destination k and shipping it back to origin j). Tosum up, exporter i is constrained in destination j, if the above inequality holds for at least oneof the other I − 1 destination markets k (excluding market j). Conversely, a producer from i isunconstrained in j, if and only if the above inequality does not hold (and hence the arbitrageconstraint is not binding) for any of the I − 1 other destinations.

Numerical analysis. We use the model by Simonovska (2015) who introduces Stone-Gearypreferences into the multi-country heterogeneous firm model. Her model provides a useful frame-work for our purpose, since Stone-Geary preferences belong to the class of utility functions (stud-ied in section 5) where arbitrage constraints may, in principle, be binding. Moreover, there isnow a well-established approach to quantifying this type of models (exemplified by Simonovskaand Waugh, 2014, whose data we use). Notice that the prices will be unconstrained monopolyprices, as Simonovska (2015) does not consider arbitrage. We will use the quantified model tocompute implied relative prices and trade costs and to check then if and how often the arbitrage

26

constraint (9) holds.The Simonovska (2015) model features many countries, indexed by i = 1, ..., I, that differ

in population size Pi and that face exporter-destination-specific trade costs τij , where we setτii = 1. It also allows for heterogenous firms within countries, which differ in productivity a

drawn from a (country-specific) Pareto distribution, Gi(a) = 1 − (bi/a)θ. All countries havethe same θ but differ in the parameter bi. Ceteris paribus, countries with a higher bi are moreproductive (and hence richer) than other countries. The utility function takes the Stone-Gearyform v(c) = log(c + γ) − log γ, where γ > 0 is a normalization constant to ensure v(0) = 0.Utility is the same for all goods and countries.

Since arbitrage is ruled out, firms set the unconstrained monopoly price in each country.Under the maintained assumptions the price in destination j charged by a country-i firm withproductivity a is

pij(a) = (τikWi/a)12 (WjLjF (θ + 1) (1 + 2θ) /γ)

12(1+θ)

(I∑

ν=1

LνPν (bν)θ (τνjWν)−θ)− 1

2(1+θ)

whereWiLi is the income level of the representative consumer in country i. From this expression,the relative price in destinations j and k of a firm producing in country i is given by

pij(a)

pik(a)=

(WjLjWkLk

) 12(θ+1)

(τijτik

) 12

(∑Iν=1 LνPνbθν (τνjWν)−θ∑Iν=1 LνPνbθν (τνkWν)−θ

)− 12(θ+1)

, (10)

where the last term in equation (10) captures relative market sizes of j and k. Note thatthe relative price in (10) is independent of the firm’s productivity a. This is a consequenceof the Stone-Geary assumption and does not hold generally with non-homothetic preferences.Simonovska (2015) shows that the expenditure share in j for goods produced in i is

λij =LiPibθi (τijWi)

−θ∑Iv=1 LνPvbθv (τvjWv)

−θ , (11)

which allows us rewrite equation (10) as

pij(a)

pik(a)=

(WjLjWkLk

) 12(θ+1)

(τijτik

) 2θ+12(θ+1)

(λijλik

) 12(θ+1)

. (12)

Equations (10) and (12) will be central in what follows since they allow us to compute the pricethat a country-i producer charges in destination j relative to the price charged in destination kunder the assumption that there is no international arbitrage. We can then compare this relativeprice to the trade costs between k and j to check if there is an incentive to buy the good cheaplyin k, ship it to j and undercut there the country-i producer. Note that (10) and (12) correspondto equations (22) and (24) in Simonovska (2015).

27

Data and baseline numerical analysis. In our baseline numerical analysis we use equation(12). We therefore need values for the parameters/variables WjLj , τij , λij , and θ. We use thedataset of Simonovska and Waugh (2014) that contains I = 123 countries for the year 2004.23 Tomeasure the above parameters/variables we proceed as follows: (i) as a measure of WjLj , we useper capita income of country j, which can be taken directly from the dataset. (ii) As a measureof λij , we use imports of j from i as a fraction of the manufacturing absorption of country j(i.e. total manufacturing output minus net exports). Simonovska and Waugh (2014) computethese shares based on source data from the UN Comtrade database and UNIDO. (iii) Tradecosts τij cannot be directly observed; we obtain estimates for τij by using the gravity approachof Simonovska and Waugh (2014).24 In principle, this method may generate trade costs belowunity. When this happens, we set τij = 1. Note that in our context, this is a conservative choice,since lower trade costs would make arbitrage more likely. (iv) We are agnostic about the specificvalue of the Pareto parameter θ. We provide results for θ = 2, 4, 6, 8, which covers the range ofestimates provided by the literature.

In the online appendix, we perform a number of robustness checks to explore the sensitivityof our findings with respect to alternative choices for (i) - (iii) above. We also present the resultsbased on equation (10) instead of (12). (Data and programs to derive these estimates and theresults shown below are provided in an online package.)

Based on the above measures, we compute the relative prices according to (12) for all countrytriples (i, j, k) by combining the observed per capita incomes and expenditure shares with theestimated trade costs. We then use these relative prices and the estimated trade costs to checkif the arbitrage condition (9) is binding. Note that the price ratio (12) goes toward infinitywhenever the trade flow from i to k is zero. In this case the arbitrage condition automaticallybecomes binding. To avoid inflating our results by this, we focus in the baseline specification onpositive trade flows.

Baseline results. An exporter from country i is subject to arbitrage in destination j, if thearbitrage condition (9) holds for at least one of the I − 1 other destinations. This suggests the

23We thank Michael Waugh for providing the dataset. For details on the dataset see the data appendix ofSimonovska and Waugh (2014).

24Simonovska and Waugh (2014) specify trade costs as log τij = α0dk,ij + α1bij + α2exi where dk,ij measuresthe distance between countries i and j (measured in 6 discrete intervals); bij indicates a common border; andexi indicates that i is the exporter in the respective trade relation (allowing for asymmetric trade cost). Usingτjj = 1 yields an empirically implementable gravity equation

log

(λijλjj

)= log

(LiPibθiW−θi

)︸ ︷︷ ︸

log Si

− log(LjPjbθjW−θj

)︸ ︷︷ ︸

log Sj

− θα0dk,ij − θα1bij − θα2exi + νij ,

where the first two terms are captured by a country effect and vij is an error term. Note that because the countryeffect is restricted to be the same when a country is the exporter as when it is the importer, one can separatelyidentify the exporter fixed effect, θα2, and the country effect, logSi. Estimating this equation yields estimatesθα0, θα1, θα2, and logSi. The estimated coefficients exactly replicate the results of Simonovska and Waugh(2014) presented in their online appendix. With an assumption for the Pareto parameter θ, we can back outα0, α1, α2 and predict trade costs as τij = exp (α0dk,ij + α1bij + α2exi). Also, by combining the predicted tradecost (scaled by the Pareto parameter) with the exponential of the estimated country effects we can compute theelement LνPνbθν (τνjWν)

−θ = Sν τ−θνj for all ν and j. These elements can be then be used when implementing

equation (10) and also when computing model-implied expenditure shares according to equation (11).

28

following two measures to quantify the relevance of the arbitrage channel:(i) a count measure: the fraction of exporter-destination pairs where the exporter is subject

to arbitrage, and(ii) a volume measure: the value of exports among constrained exporter-destination pairs

relative to the total global volume of exports.There are in total I × (I − 1) = 15, 006 potential bilateral trade relations, of which 10, 636

flows feature positive (non-zero) trade. Among these exporter-destination pairs, according tothe baseline numerical analysis shown in Panel a of Table 2, more than 20 percent are priceconstrained. This estimate varies little with the choice of the Pareto parameter θ. When we setθ = 2 (close to Jung et al. 2015), we find that 2, 199 out of the 10, 636 export flows, or 20.7

percent are price constrained. When we increase this value to θ = 8 (close to Eaton and Kortum2002), the estimate increases only slightly to 21.9 percent. Changing θ has little quantitativeimpact, since both sides (9) move in the same direction. When θ increases, both the elasticityof relative prices with respect to per capita income differences, (2(θ + 1))−1, and trade costsdecrease.

Table 2

Panel a also displays both the number of direct and indirect cases, that lead to constrainedexporters. When θ = 4, inequality (9) holds for 32 country pairs (direct arbitrage) and for 3, 726

country triples (indirect arbitrage). The fact that there are few directly and many indirectlybinding arbitrage constraints is per se not surprising as the number of country triples (whereindirect arbitrage can potentially occur) is an order of magnitude larger than the number ofcountry pairs.25 Notice also that there are more indirect arbitrage possibilities than constrainedexporter-destination pairs. This is because one exporter-destination pair can be subject toindirect arbitrage through several third countries. The numerical analysis finds that the averageconstrained exporter-destination pair is price constrained through about 1.5 third countries.

In Panel b of Table 2, we calculate the export volume that is subject to a binding arbitrageconstraint. Irrespective of the particular value of θ, our numerical analysis suggests that about 45percent of total world trade is subject to arbitrage. Interestingly, the volume measure indicatesthat arbitrage is of even higher importance than indicated by the count measure. This suggeststhat large export flows are more likely to be constrained.

We conclude that the numerical analysis of a multi-country model, in which preferences aresuch that the arbitrage constraint can in principle become binding, indicates that the arbitragechannel is quantitatively relevant: the typical exporter is price-constrained on 20 percent of itsdestinations and about 45 percent of world trade occurs among constrained exporter-destinationpairs.

In the online appendix, we also show separately for each of the 123 exporters in the data set,the number and volume of constrained destinations. For instance, the US, Japan, and China

25Of course, indirect arbitrage is only counted, when it emerges through a third country k that is actuallyserved by producer i. This means that indirect arbitrage threats are only considered for the subset of theI × (I − 1)× (I − 1) = 1, 830, 732 triples, where both the flows from i to j and from i to k is non-zero.

29

export to all other (122) countries and are constrained in 8, 10, and 13 destinations, respectively.In contrast, the large European exporters, Germany, France, and the UK also export to all othercountries and are constrained in 67, 97 and 85 destinations, respectively. The larger numberof binding destinations for European exporters is partly due to the high integration (low tradecosts) within Europe. This leads to a disproportionate share of indirect arbitrage via cheaperEuropean destinations.

Robustness. In the online appendix, we check the robustness of our results with respect toalternative ways to measure the crucial parameters/varibles. (i) To calculate expenditure sharesfrom observed data, we can use GDP in the denominator rather than manufacturing absorption.26

(ii) For the trade costs, we can allow fitted trade costs τij to fall short of unity (while the baselinesets estimated trade costs below unity to 1). (iii) To quantify WiLi, we can calculate model-consistent wage rates using the balanced trade condition, WiLiPi =

∑Ij=1 λijWjLjPj . This can

be done using empirically observed expenditure shares λij or model-implied expenditure sharesλij (which are computed using the procedure sketched in footnote 24 above). (iv) We alsopresent the results when using equation (10) instead of (12), which is equivalent to replacing theempirically observed expenditure shares in equation (12) with the model-implied expenditureshares λij . (v) Finally, for each of the alternative choices in (i)-(iv) we iterate over the differentvalues of the Pareto parameter θ = 2, 4, 6, 8. In total, this yields 2×2×3×2×4 = 96 alternativeways to calculate the outcomes of interest (including our baseline specification).

While the particular values for the count and volume measures vary across the various specifi-cation, two robust conclusions emerge. First, there is always a substantial fraction of constrainedexporters, ranging from 12.5 to 50.8 percent. Second, in all specifications, the share of constrainedexports (volume measure) is substantial and larger than the share of constrained markets (countmeasure). This suggests that arbitrage is more important for larger exporters, ranging from 43.0to 75.4 percent. We conclude that the results of our baseline numerical analysis are robust.

Discussion. Notice that the above numerical exercise is tentative and clearly needs to be takenwith caution. Here we emphasize three points which have to be kept in mind when interpretingthe results. First, the baseline numerical analysis is based on observed and strictly positive(non-zero) trade flows. This is clearly in the spirit of our arbitrage model, which emphasizes thelimits to price setting for exporters with big price differences and low trade costs. However, ourmodel of arbitrage also emphasizes the relevance of arbitrage threats for export zeros (that letfirms abstain from exporting). In the online appendix, we compute relative prices for zero tradeflows using equation (10) and country fixed effects from the gravity regression (the approach issketched out at the end of footnote 24). Relative prices for zero exports can be calculated fromequation (10) because the gravity approach of Simonovska and Waugh (2014) yields estimatesfor τij even when i does not export to j. This allows us to test whether inequality (9) holds (ordoes not hold) for export zeros. We find that the fraction of export zeros that feature bindingarbitrage lies between 6.8 percent (θ = 2) and 5.4 percent (θ = 8). One reason for the lower

26Notice that GDP is consistent with the model, but inconsistent with the data, since trade are gross flowswhile GDP is value added.

30

frequency of arbitrage among exports zeros are the rather high estimated trade costs amongthese exporter-destination pairs.

This brings us to the second issue, the rather large size of estimated iceberg costs. With θ = 8,about 55 percent of bilateral trade relationships have iceberg trade costs larger than 3, withθ = 6, 4, 2 this number increases to 75, 90, and 95 percent, respectively. High estimated icebergcosts may reflect real-world barriers not adequately captured by the model, such as fixed costs (forestablishing a trade relationship, infrastructure, distribution networks, marketing, etc.). Thesecosts, while potentially substantial for the incumbent firm, maybe do not accrue for arbitrageurs(who may, at least partly, free-ride on incumbents). In this case, the trade costs relevant forarbitrageurs could be lower than those captured in the numerical analysis, suggesting that ourprocedure tends to underestimate the importance of arbitrage. (This could partly explain thelower relevance of arbitrage among export zeros). Clearly, other real-world features not capturedin the model may work in the opposite direction. In particular, incumbent firms may lobbyfor restricting parallel trade (pharmaceutical products are one prominent example), differentiateproducts (horizontally or vertically), or use other strategies that limit the usefulness/desirabilityof a product sold in country k for consumers in destination j, thereby reducing arbitrage threats.

A third point concerns the role of firm heterogeneity. While the Stone-Geary specificationprovides an elegant and simple framework, it implies that relative prices of a country-i exporterdo not depend on the firm’s productivity, a, see equation (12). This leads to the prediction that,if one exporter from country i is price-constrained in market j, all other exporters from i arealso constrained in that market. This artefact of the Stone-Geary specification abstracts fromimportant margins (product characteristics, product-specific trade costs) which may be relevantin practice.

8 Conclusions

This paper studies a model of international trade in which an importer’s per capita incomedetermines export zeros and prices of exported goods. This is due to a demand effect: consumersin poor countries have lower willingnesses to pay for differentiated products than consumers inrich countries. As a result, northern firms have a low incentive to export to a southern destination.Our model generates export zeros from non-homothetic preferences and does not rely on firmheterogeneity and/or fixed export-market entry costs. Hence our analysis is complementary tostandard heterogeneous-firm approaches which focus on the supply side.

A key insight of our analysis is that export zeros arise from a threat of international arbitrage.Globally active firms cannot simultaneously set low prices in the South and high prices in theNorth because this triggers arbitrage opportunities. Northern firms have two options to avoidarbitrage: (i) set a sufficiently low price in the North; or (ii) abstain from exporting to the South.These two options involve a trade-off between market size and price: firms that export globallyhave a large market but need to charge a low price; firms that sell exclusively to northern marketscan charge a high price but have a smaller market. The equilibrium of our model is characterizedby Linder-effects, a situation where similarity in per capita incomes increases trade intensity

31

between two countries. The model also generates interesting welfare effects. While rich countriesalways gain from a trade liberalization, poor countries may lose. Lower trade costs tighten thearbitrage constraint and this induces northern firms not to export to poor destinations, thusreducing the menu of supplied goods and harming welfare of households in the South.

We argue that the arguments put forth in this paper are potentially empirically relevant.Our model predicts a positive relationship between the export probability of rich exporters andthe per capita income of a potential destination. While this is clearly supported by the data, itdoes not necessarily arise from a threat of arbitrage but could also be due too high export costs.

To shed more specific light on the potential relevance of the arbitrage constraint, we pursuea model-based approach. We explore a model of non-homothetic preferences featuring manycountries and heterogenous firms (Simonovska 2015). This model makes predictions for therelative price of a given product between any two locations – under the assumption that firms donot take arbitrage constraints into account. We pursue a simple consistency check and explorewhether and to which extent the predicted relative prices violate the arbitrage constraint. Wefind that arbitrage constraints are indeed violated in many trade relations which suggests thatinternational arbitrage is potentially relevant.

The above consistency check is based on the predictions of a model that does not takearbitrage constraints into account. Solving a full-fletched multi-country model with supply anddemand heterogeneities that takes arbitrage constraints into account turns out complex and isbeyond the scope of this paper.27 However, our analysis suggests that accounting for arbitrage inmodels of monopolistic competition and international trade is an interesting direction for futureresearch. The challenge is to appropriately disentangle supply and demand effects and assesstheir relative importance. This seems particularly relevant for a better understanding of howrapidly growing per capita incomes in China, India and other emerging markets affect tradepatterns and the international division of labor.

27If arbitrage is ruled out, a firm optimizes country by country. In contrast, if arbitrage is allowed, the firmoptimizes for all countries simultaneously. In fact, it does not only optimize the price in each country taking intoaccount potential arbitrage flows, but also optimizes the set of countries that it supplies. While this problemcan be clearly characterised, we were not able to derive general equilibrium expressions that take empiricallyimplementable forms.

32

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37

A Proof of Proposition 1

Part b). This follows from calculating the derivatives of φ with respect to LP

∂φ

∂LP=

2LRPRωPP

(LRPR + ωLPPP )2− 4LRPRωLPPP

(LRPR + ωLPPP )3ωPP =

φ

LP

(1− 2ωLPPP

LRPR + ωLPPP

),

and with respect to PP

∂φ

∂PP=φ(

1 + ∂ω∂PP

PPω

)PP

(1− 2ωLPPP

LRPR + ωLPPP

),

where ∂ω∂PP

PPω > 0.

Part c). A given increase in LPPP has a stronger impact on φ if it comes from PP ratherthan from LP if ∂φ/∂ logLP =

(∂φ/∂LP

)LP < ∂φ/∂ logPP =

(∂φ/∂PP

)PP . This is true

since ∂ω∂PP

PPω > 0.

Part d). This follows from the derivative of φ with respect to τ

∂φ

∂τ=φ∂ω∂τω

(1− 2ωLPPP

LRPR + ωLPPP

).

B Proof of Proposition 2

Part b) follows from the derivatives of φ with respect to LP and PP . It is straightforward to seethat ∂φ/∂LP > 0. To calculate ∂φ/∂PP we need to take into account that ω depends on PP

∂φ

∂PP=

−1

PR (τ + PP /PR)φ+

1 + ∂ω∂PP

PPω

PPLRPR

LRPR + ωLPPPφ,

hence an increase in PP increases trade intensity φ when PP is small and vice versa.Part c). We need to show that the volume of trade increases with PP less than proportionally.

The argument in the text was made without considering that PP increases ω. It remains to showthat, taking account of the impact of PP on ω, an increase in PP reduces per capita imports.We have sign(∂pPNR

T /∂PP ) = sign(∂ log(pPNRT )/∂PP ) < 0. Calculating pPNR

T , taking logsand the derivative with respect to PP reveals that ∂pPNR

T /∂PP < 0 if

− 1

τPR + PP+

τ

aF + PR + τPP− 1

aF + τPR + PP< 0.

Multiplying by aF + PR+ τPP yields

−aF + PR + τPP

τPR + PP+τ(aF + PR + τPP )

aF + PR + τPP− aF + PR + τPP

aF + τPR + PP< 0⇐⇒ −pP +

τ − ωa

< 0,

which holds true because pP > τ/a.

38

Part d). We note that sign(∂φ/∂τ) = sign(∂ log φ/∂τ). Taking logs of the expression for φand the derivative with respect to τ yields

sign(∂φ/∂τ) = sign

(1

τ− 1

τ + PRPP

+ω′(τ)

ω(τ)− ω′(τ)

ω(τ)·

ω(τ)LP

LR

ω(τ)LP

LR+ PRPP

)> 0,

which, using ω(τ)LP /LR < τ and ω′(τ)τω(τ) > −1, implies

sign(∂φ/∂τ) = sign

[(1 +

ω′(τ)τ

ω(τ)

)(1− τ

τ + PRPP

)]> 0.

C Proof of Proposition 3

Part a). In an arbitrage equilibrium we have pP =(aF + PR + τPP

)/(aτPR + aPP

). Country

-R firms export if pP ≥ τ/a or, equivalently,(aF + PR + τPP

) (τPR + PP

)−1 ≥ τ . Solvingthat latter equation for τ yields the trade condition. (Notice that, if the trade condition holdsfor country -R firms, it also holds for country -P firms, as we have pRT = τpP > pP .)

Part b). Under full trade we have pP = ωLP(aF + PR + τPP

) (aPRLR + aωPPLP

)−1 ≥τ/a or

(ωLP /LR

) (aF/PR + 1

)≥ τ . But since full trade occurs only when ωLP /LR ≥ 1/τ , the

trade condition follows.

D Two regions: n rich and m poor countries

In an arbitrage equilibrium, the price of globally traded goods is pRT = τpP in the North. Zeroprofit constraints of globally traded goods are

pPmPP + τpPnPR =

(F +

P i + τP−i

a

)W i, i = R,P.

where where P−R = (n − 1)PR + mPP and P−P = nPR + (m − 1)PP . The prices of globallytraded goods can be directly calculated pP = (aF+PR+τP−R)/(amPP+aτnPR) and pRT = τpP .

The zero profit conditions for goods exclusively traded in the North are

pRNnPR =

(F +

PR + τ(n− 1)PR

a

)WR,

and the price of these goods follows immediately pRN = WR(aF + PR + τ(n − 1)PR)/(anPR).

From the zero profit conditions of globally traded goods we can calculate relative wages betweenNorth and South

ω ≡ WP

WR=aF + τP−R + PR

aF + PP + τP−P.

39

The resource constraints are

LPPP = NP

(F +

PP + τP−P

a

)for a poor country, and

LRPR = NRT

(F +

PR + τP−R

a

)+NR

N

(F +

PR + τ(n− 1)PR

a

)for a rich country.

Each R-country imports all goods produced worldwide, while each P -country imports only asubset of these goods. Hence the aggregate trade balance between the North and the South hasto be balanced in equilibrium.28 This implies

τNPPR = NRT PP .

From the resource constraints and the trade balance condition we get closed-form solutions forNP , NT

R , and NRN . This gives welfare of rich and poor households

UR (τ) = mNP + nNRT + nNR

N =aLP

(mPP + τnPR

)aF + PP + τP−P

+a(LR − τωLP

)nPR

aF + PR + τ(n− 1)PR,

and

UP (τ) = mNP + nNRT =

aLP(mPP + τnPR

)aF + PP + τP−P

.

We see that that ∂UR (τ) /∂τ < 0 and ∂US (τ) /∂τ ≤ 0 when aF < (m−1)PP (1+mPP /(nPR)).It also follows that ∂UR (τ) /∂τ < ∂US (τ) /∂τ , i.e. a trade liberalization benefits the richcountry more.

Finally, let us calculate trade intensity. The value of North-North trade is given by

2(n− 1)(pRNN

RN + pRTN

RT

)nPR = 2(n− 1)

(LR − ωτLP mPP

mPP + τnPR

)PR.

The value of South-South trade is

2(m− 1)pPNPmPP = 2(m− 1)mPP

mPP + τnPRωLPPP

and the value of North-South trade is

2mpPNPnPR = 2mnτPR

mPP + τnPRωLPPP

28Due to the symmetry of our set-up, the volume of bilateral trade is undetermined. One of the Northerncountries could produce predominantly (or exclusively) goods that are consumed only in the North, while theother Northern country produces mainly (or exclusively) goods that are consumed worldwide. In that case,the first Northern country runs a trade surplus with the other Northern country and a trade deficit with bothSouthern countries taken together. Such trade imbalances cannot occur between the Southern countries, sinceeach Southern country consumes all goods the other Southern country produce, meaning that the South-Southtrade flows are of the same magnitude in either direction. However, each Southern country may run a surpluswith one of the Northern countries that is balanced by a deficit with the other Northern country. Notice furtherthat all bilateral trade flows are equalized in a full trade equilibrium since all households in each country consumeall goods that are produced worldwide.

40

This allows us to calculate trade intensity φ, the value of world trade relative to world GDP as

φ = 2(n− 1)

(pRNN

RN + pRTN

RT

)nPR + (m− 1)pPNPmPP +mpPNPnPR

nLRPR +mωLPPP

which, using the above formulas, can be expressed as

φ = 2mωLPPP

nLRPR +mωLPPP

((m− 1)PP + nτPR

mPP + nτPR

)+ 2

(n− 1)(LR − τωLP mPP

mPP+τnPR

)PR

nLRPR +mωLPPP.

φ = 2mωLPPP

nLRPR +mωLPPP

((m− 1)PP + nτPR

mPP + nτPR

)−2

(n− 1)τωLP mPPmPP+τnPRP

R

nLRPR +mωLPPP+2

(n− 1)LRPR

nLRPR +mωLPPP.

φ = 2mωLPPP

nLRPR +mωLPPP(m− 1)PP + τPR

mPP + nτPR+ 2

(n− 1)LRPR

nLRPR +mωLPPP.

When m = 1 and n = 1 we get

φ = 2ωLPPP

LRPR + ωLPPPτPR

τPR + PP.

Unlike in the arbitrage equilibrium of the two-county case, trade intensity may decrease in τ .This is when a reduction in τ increases South-South and North-North trade more strongly thanit reduces North-South trade.

E Equilibrium with general preferences

The arbitrage equilibrium. Here we state the full system of equations that characterize anarbitrage equilibrium with non-traded goods. Households choose consumption levels to maximizeutility. This implies marginal rates of substitution

v′(cRR)

v′(cRP )=pRRpRP,

v′(cPR)

v′(cPP )=pPRpPP,

v′(cRR)

v′(cNR )=pRRpNR

.

Firms set prices to maximize profits. Firms that sell exclusively on the home market set theunconstrained monopoly price

pNR = µ(cNR )1

a.

Exporting firms set prices to avoid arbitrage

pRP = τpPP , pRR = τpPR.

41

which leads to first-order conditions29

τpPP − ω/a

pPP

(−v′(cRP )

v′′(cRP )

)+pPP − ω/a

pPP

(−v′(cPP )

v′′(cPP )

)PP

PR= τcRP + cPP

PP

PR,

τpPR − 1/a

τpPR

(−v′(cRR)

v′′(cRR)

)+pPR − τ/a

pPR

(−v′(cPR)

v′′(cPR)

)PP

PR= cRR + τcPR

PP

PR.

The resource constraints are

LP = NP

(F + PRτcRP /a+ PP cPP /a

),

LR = NTR

(F + PRcRR/a+ PP τcPR/a

)+NN

R

(F + PRcNR /a

),

the trade balance condition ispPRN

TRPP cPR = pRPNPPRcRP ,

and the zero-profit conditions are

PP cPP(pPP − ω/a

)+ PRcRP

(pRP − τω/a

)= ωF.

PRcRR(pRR − 1/a

)+ PP cPR

(pPR − τ/a

)= F,

PRcNR(pNR − 1/a

)= F,

In sum, the arbitrage equilibrium has 14 equations in 14 unknowns: quantities (cPP , cPR, c

RR, c

RP , c

NR ),

prices (pPP , pPR, p

RR, p

RP , p

NR ), firm measures (NP , N

TR , N

NR ), and the relative wage ω.

Full trade equilibria. As mentioned in the main text, a binding arbitrage constraint is anecessary though not sufficient condition for an arbitrage equilibrium with non-traded goodssince consumers can now respond also along the intensive margin. There are three types of fulltrade equilibria: (i) both P - and R-firms are price-constrained; (ii) P -firms are price-constrainedwhile R-firms set the monopoly price; and (iii) firms in both countries set the monopoly price.30

ad (i). When both firms are price-constrained but all goods are traded, all equations areidentical except that NN

R = cNR = 0 and pNR do not exist. The system reduces to 11 equations.ad (ii). When P -firms are price constrained but R-firms are not, we have pRR = µ(cRR)/a and

pPR = µ(cPR)τ/a while pRP and pPP are still determined as above.ad (iii). When firms in both countries are unconstrained, also P -firms set the monopoly price

pPP = µ(cPP )ω/a and pRP = µ(cRP )ωτ/a.29These conditions derive from maximizing the profit functions for country-P and country-R producers, i.e.PP cPP

(pPP − ω/a

)+PRcRP

(pRP − τω/a

)and PRcRR

(pRR − 1/a

)+PP cPR

(pPR − τ/a

), subject to the above arbitrage

constraints. Moreover, we use the fact that households’ demand functions derive from v(c) = λp which implies∂c/∂p = (1/p)v′(c)/v′′(c).

30Notice that the (unconstrained) price gap of country-P firms between market P and market R is higher thanthe corresponding price gap for country-R firms. This is because country-P firms have low (high) costs and low(high) demand on the home (foreign) market. This is different from the situation of country-R firms. They havehigh (low) costs and low (high) demand on the foreign (home) market. This implies that country-P firms getprice-constrained first, and an equilibrium, where country-R firms are price-constrained - but country-P firms arenot - cannot exist.

42

F Proof of Proposition 7

We determine the autarky equilibrium and ask under which conditions an entrepreneur hasincentives to sell his products abroad. Setting W = 1, optimal monopolistic pricing impliesp = µ(c)/a. With free entry, profits PR(pRa − 1/a)cRa must equal set up costs F

aF/PR =(µ(cRa )− 1

)cRa

The equilibrium is symmetric for all firms, hence the resource constraint reads

LR = NRa

(F + PRcRa /a

)Solving for cRa and NR

a , we see that cRa does not depend on LR. Hence when the two countriesdiffer only in Li but have equal populations, intensive consumption levels under autarky areidentical between the two countries, cRa = cPa . Selling one marginal unit abroad at price v′(0)/λPa ,

allows the purchase of v′(0)/(λPa pPa ) foreign goods. Since λPa = v′(cPa )/pPa and cRa = cPa this is

equal to v′(0)/v′(cRa ) > 1. Reselling this (new) product at home, yields a price v′(0)pRa /v′(cRa )

minus trade costs. Hence, this strategy is profitable if[v′(0)pRa /v

′(cRa )]·[v′(0)/v′(cRa )

]> τ2.

Expressing pRa in terms of cRa , we get the condition of the Proposition.

43

Figure 1: Demand function

1

1)( jx

)( jp

Figure 1: Demand function

Figure 2: Full trade and arbitrage equilibrium

RP LL1

A

10

F

Figure 2: Full trade and arbitrage equilibrium

1/ RaF P

44

Figure 3: Welfare and trade costs

RP UU ,

PR LL1

panel a

RP UU ,

1

panel b

Figure 3: Welfare and trade costs

1/ RaF P1/ RaF P

(a)

RP UU ,

PR LL1

panel a

RP UU ,

1

panel b

Figure 3: Welfare and trade costs

1/ RaF P1/ RaF P

(b)

45

Table 1: Extensive margin of U.S. exports, 2007(1) (2) (3) (4) (5)All All Pop>1m All AllHS6 HS6 HS6 HS4 HS2

Mean dependent variable 0.391 0.391 0.399 0.576 0.731

Log importer GDP 0.064∗∗∗ 0.070∗∗∗ 0.089∗∗∗ 0.076∗∗∗ 0.061∗∗∗

(0.011) (0.010) (0.010) (0.011) (0.009)

Log importer GDP per capita 0.085∗∗∗

(0.014)

Per capita income USD 385–999 -0.265∗∗∗ -0.205∗∗∗ -0.270∗∗∗ -0.178∗∗∗

(0.064) (0.066) (0.067) (0.065)

Per capita income USD 1,000–1,999 -0.262∗∗∗ -0.226∗∗∗ -0.249∗∗∗ -0.145∗∗

(0.067) (0.068) (0.071) (0.060)

Per capita income USD 2,000–3,999 -0.237∗∗∗ -0.233∗∗∗ -0.232∗∗∗ -0.163∗∗∗

(0.065) (0.063) (0.066) (0.049)

Per capita income USD 4,000–7,999 -0.116∗ -0.146∗∗ -0.076 -0.035(0.069) (0.066) (0.068) (0.047)

Per capita income USD 8,000–15,999 -0.128∗ -0.149∗∗ -0.104 -0.089∗

(0.068) (0.064) (0.067) (0.051)

Per capita income USD 16,000–31,999 -0.034 -0.030 -0.017 -0.008(0.064) (0.061) (0.060) (0.041)

Per capita income USD 32,000– ref ref ref ref

Trade cost indicators Yes Yes Yes Yes YesHS fixed effects Yes Yes Yes Yes Yes

Adjusted R2 0.424 0.423 0.442 0.431 0.417N 169,020 169,020 147,736 42,255 9,045

Notes: Estimates based on a linear probability model, ?, ??, ??? denotes statistical significance at the 10%, 5%,1% level, respectively. Standard errors are clustered on importer level. Year is 2007. Omitted category of incomeper capita groups is above USD 32,000. Trade cost indicators include log of distance between exporter’s andimporter’s capital, dummy for a common border, dummy for importer being an island, dummy for importer beinglandlocked, dummy for importer and exporter ever having had colonial ties, dummy for currency union betweenimporter and exporter, dummy for importer and exporter sharing a common legal system, dummy for religioussimilarity, dummy for importer and exporter having a free trade agreement, and dummy for importer and exportersharing a common language.

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Table 2: Number of constrained exporters and constrained export volumeθ = 2 θ = 4 θ = 6 θ = 8

Panel a: Number of constrained exportersNumber positive trade flows 10,636 10,636 10,636 10,636Number constrained flows 2,199 2,239 2,295 2,324Fraction constrained 0.207 0.211 0.216 0.219Direct arbitrage 28 32 37 37Indirect arbitrage 3466 3726 3903 4022

Panel b: Constrained export volumeWorld trade volume (m) 6,829,931 6,829,931 6,829,931 6,829,931Constrained volume (m) 3,113,948 3,077,943 3,106,796 3,136,772Share constrained volume 0.456 0.451 0.455 0.459Direct constrained volume (m) 1,315,237 1,375,793 1,489,080 1,489,080Share direct constrained volume 0.193 0.201 0.218 0.218

Notes: The data is described in the Data Appendix of Simonovska and Waugh (2014). Bilateral trade-flow data are from UN Comtrade for the year 2004 (for a sample of 123 countries, restricted to manu-facturing trade flows only). Manufacturing production data for 2004 is from UNIDO where it exists andimputed for all other countries.

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